Form N-Q

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, DC 20549

FORM N-Q


QUARTERLY SCHEDULE OF PORTFOLIO HOLDINGS OF REGISTERED MANAGEMENT INVESTMENT COMPANY

Investment Company Act file number         811-7606         

        Nuveen Connecticut Premium Income Municipal Fund         
(Exact name of registrant as specified in charter)


        333 West Wacker Drive, Chicago, Illinois 60606         
(Address of principal executive offices) (Zip code)


Jessica R. Droeger—Vice President and Secretary
        333 West Wacker Drive, Chicago, Illinois 60606         
(Name and address of agent for service)

Registrant's telephone number, including area code:         312-917-7700        

Date of fiscal year end:            05/31          

Date of reporting period:          08/31/05         

Form N-Q is to be used by management investment companies, other than small business investment companies registered on Form N-5 (§§ 239.24 and 274.5 of this chapter), to file reports with the Commission, not later than 60 days after the close of the first and third fiscal quarters, pursuant to rule 30b1-5 under the Investment Company Act of 1940 (17 CFR 270.30b1-5). The Commission may use the information provided on Form N-Q in its regulatory, disclosure review, inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q, and the Commission will make this information public. A registrant is not required to respond to the collection of information contained in Form N-Q unless the Form displays a currently valid Office of Management and Budget (“OMB”) control number. Please direct comments concerning the accuracy of the information collection burden estimate and any suggestions for reducing the burden to the Secretary, Securities and Exchange Commission, 450 Fifth Street, NW, Washington, DC 20549-0609. The OMB has reviewed this collection of information under the clearance requirements of 44 U.S.C. § 3507.

Item 1. Schedule of Investments

  Portfolio of Investments (Unaudited)
Nuveen Connecticut Premium Income Municipal Fund (NTC)
August 31, 2005

  Principal                  
  Amount (000)   Description(1)    Optional Call Provisions*   Ratings**     Market Value 
      Consumer Staples - 2.8% (1.9% of Total Investments)               
$   1,580    Puerto Rico, The Children's Trust Fund, Tobacco Settlement Asset-Backed Refunding Bonds, Series    5/12 at 100.00    BBB    $   1,631,903 
      2002, 5.375%, 5/15/33               
  600    Guam Economic Development Authority, Tobacco Settlement Asset-Backed Bonds, Series 2001B, 5.500%,    5/11 at 100.00    Baa3      617,832 
      5/15/41               
      Education and Civic Organizations - 38.4% (26.3% of Total Investments)               
      Connecticut Higher Education Supplemental Loan Authority, Revenue Bonds, Family Education Loan               
      Program, Series 1996A:               
  745    5.800%, 11/15/14 (Alternative Minimum Tax) - AMBAC Insured    11/06 at 102.00    AAA      756,816 
  470    5.875%, 11/15/17 (Alternative Minimum Tax) - AMBAC Insured    11/06 at 102.00    AAA      477,703 
  415    Connecticut Higher Education Supplemental Loan Authority, Revenue Bonds, Family Education Loan    11/09 at 102.00    AAA      417,901 
      Program, Series 1999A, 6.000%, 11/15/18 (Alternative Minimum Tax) - AMBAC Insured               
  900    Connecticut Higher Education Supplemental Loan Authority, Revenue Bonds, Family Education Loan    11/11 at 100.00    Aaa      954,882 
      Program, Series 2001A, 5.250%, 11/15/18 (Alternative Minimum Tax) - MBIA Insured               
  1,500    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Loomis Chaffee School,    7/06 at 102.00    AAA      1,545,390 
      Series 1996C, 5.500%, 7/01/16 - MBIA Insured               
  1,900    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Fairfield University,    7/08 at 102.00    AAA      2,012,708 
      Series 1998H, 5.000%, 7/01/23 - MBIA Insured               
  2,920    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Connecticut College, Series    7/07 at 102.00    AAA      3,101,449 
      1997C-1, 5.500%, 7/01/20 - MBIA Insured               
  2,115    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Connecticut State    11/15 at 100.00    AAA      2,345,154 
      University System, Series 2005H, 5.000%, 11/01/17 - FSA Insured               
  1,250    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Fairfield University,    7/09 at 101.00    AAA      1,340,113 
      Series 1999I, 5.250%, 7/01/25 - MBIA Insured               
  750    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Horace Bushnell Memorial    7/09 at 101.00    Aaa      815,775 
      Hall, Series 1999A, 5.625%, 7/01/29 - MBIA Insured               
  1,000    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Connecticut State    No Opt. Call    AAA      1,111,330 
      University System, Series 2003F, 5.000%, 11/01/13 - FSA Insured               
  500    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Trinity College, Series    7/11 at 101.00    AAA      528,525 
      2001G, 5.000%, 7/01/31 - AMBAC Insured               
  650    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Loomis Chaffee School,    7/11 at 101.00    A2      710,190 
      Series 2001D, 5.500%, 7/01/23               
  1,375    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Trinity College, Series    7/14 at 100.00    AAA      1,491,848 
      2004H, 5.000%, 7/01/21 - MBIA Insured               
  450    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Greenwich Academy, Series    3/11 at 101.00    AAA      474,084 
      2001B, 5.000%, 3/01/32 - FSA Insured               
  2,000    Connecticut Health and Educational Facilities Authority, Revenue Bonds, University of Hartford,    7/12 at 101.00    AA      2,128,140 
      Series 2002E, 5.250%, 7/01/32 - RAAI Insured               
  1,500    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Yale University, Series    7/09 at 100.00    AAA      1,582,800 
      2002W, 5.125%, 7/01/27               

  1,500    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Yale University, Series   7/13 at 100.00    AAA        1,580,745 
      2003X-1, 5.000%, 7/01/42              
  925    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Brunswick School, Series   7/13 at 100.00    AAA      982,480 
      2003B, 5.000%, 7/01/33 - MBIA Insured              
  1,000    University of Connecticut, Student Fee Revenue Refunding Bonds, Series 2002A, 5.250%, 11/15/19 -   11/12 at 101.00    AAA      1,117,320 
      FGIC Insured              
  1,100    University of Connecticut, General Obligation Bonds, Series 2003A, 5.125%, 2/15/21 - MBIA Insured   2/13 at 100.00    AAA      1,206,557 
      University of Connecticut, General Obligation Bonds, Series 2004A:              
  1,000    5.000%, 1/15/18 - MBIA Insured   1/14 at 100.00    AAA      1,094,710 
  2,000    5.000%, 1/15/19 - MBIA Insured   1/14 at 100.00    AAA      2,184,880 
  1,220    University of Connecticut, General Obligation Bonds, Series 2005A, 5.000%, 2/15/17 - FSA Insured   2/15 at 100.00    AAA      1,350,174 
 
      Healthcare - 11.4% (7.8% of Total Investments)              
  2,000    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Stamford Hospital, Series   7/09 at 101.00    Aaa      2,086,060 
      1999G, 5.000%, 7/01/24 - MBIA Insured              
  3,000    Connecticut Health and Educational Facilities Authority, Revenue Refunding Bonds, Middlesex Health   7/07 at 101.00    Aaa      3,082,530 
      Services, Series 1997H, 5.125%, 7/01/27 - MBIA Insured              
  2,000    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Eastern Connecticut Health   7/10 at 101.00    AA      2,214,300 
      Network, Series 2000A, 6.000%, 7/01/25 - RAAI Insured              
  500    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Bristol Hospital, Series   7/12 at 101.00    AA      547,300 
      2002B, 5.500%, 7/01/21 - RAAI Insured              
      Connecticut Health and Educational Facilities Authority, Revenue Bonds, Griffin Hospital, Series              
      2005B:              
  800    5.000%, 7/01/20 - RAAI Insured   7/15 at 100.00    Aa3      856,408 
  500    5.000%, 7/01/23 - RAAI Insured   7/15 at 100.00    Aa3      533,170 
 
      Housing/Multifamily - 3.7% (2.5% of Total Investments)              
  1,000    Connecticut Housing Finance Authority, Housing Mortgage Finance Program Bonds, Series 1999D-2,   12/09 at 100.00    AAA      1,049,480 
      6.200%, 11/15/41 (Alternative Minimum Tax)              
  1,865    Williamantic Housing Authority, Connecticut, GNMA Collateralized Multifamily Housing Mortgage   10/05 at 105.00    AAA      1,962,670 
      Revenue Bonds, Village Heights Apartments, Series 1995A, 8.000%, 10/20/30              
 
      Housing/Single Family - 1.3% (0.9% of Total Investments)              
  1,000    Connecticut Housing Finance Authority, Housing Mortgage Finance Program Bonds, Series 2001C,   11/10 at 100.00    AAA      1,030,280 
      5.300%, 11/15/33 (Alternative Minimum Tax)              
 
      Industrials - 2.2% (1.5% of Total Investments)              
  1,750    Connecticut Resource Recovery Authority, Revenue Bonds, American Ref-Fuel Company of Southeastern   12/11 at 102.00    Baa2      1,823,658 
      Connecticut LP, Series 1998A-I, 5.500%, 11/15/15 (Alternative Minimum Tax)              
 
      Long-Term Care - 7.0% (4.8% of Total Investments)              
  1,300    Connecticut Health and Educational Facilities Authority, FHA-Insured Mortgage Revenue Bonds, Hebrew   8/08 at 102.00    AAA      1,359,748 
      Home and Hospital, Series 1999B, 5.200%, 8/01/38              
  750    Connecticut Development Authority, First Mortgage Gross Revenue Refunding Healthcare Bonds, Church   4/07 at 102.00    BBB-      778,493 
      Homes Inc. - Congregational Avery Heights, Series 1997, 5.700%, 4/01/12              
  615    Connecticut Development Authority, First Mortgage Gross Revenue Refunding Healthcare Bonds,   9/09 at 102.00    AA      664,397 
      Connecticut Baptist Homes Inc., Series 1999, 5.500%, 9/01/15 - RAAI Insured              
      Connecticut Development Authority, Revenue Refunding Bonds, Duncaster Inc., Series 1999A:              
  1,000    5.250%, 8/01/19 - RAAI Insured   2/10 at 102.00    AA      1,062,540 
  1,000    5.375%, 8/01/24 - RAAI Insured   2/10 at 102.00    AA      1,066,890 
  800    Connecticut Development Authority, Health Facilities Revenue Refunding Bonds, Alzheimer's Resource   2/06 at 101.00    N/R      809,920 
      Center of Connecticut Inc., Series 1994A, 7.000%, 8/15/09              

    Tax Obligation/General - 24.5% (16.8% of Total Investments)              
500    Bridgeport, Connecticut, General Obligation Bonds, Series 2004C, 5.250%, 8/15/14 - MBIA Insured   No Opt. Call    AAA        563,080 
750    Bridgeport, Connecticut, General Obligation Refunding Bonds, Series 2002A, 5.375%, 8/15/19 - FGIC   8/12 at 100.00    Aaa      832,965 
    Insured              
1,000    Bridgeport, Connecticut, General Obligation Bonds, Series 2003A, 5.250%, 9/15/23 - FSA Insured   9/13 at 100.00    AAA      1,111,320 
1,900    Capitol Region Education Council, Connecticut, Revenue Bonds, Series 1995, 6.700%, 10/15/10   10/05 at 102.00    BBB      1,943,434 
1,110    Connecticut, General Obligation Bonds, Series 2004C, 5.000%, 4/01/23 - FGIC Insured   4/14 at 100.00    AAA      1,199,566 
820    Connecticut, General Obligation Bonds, Series 2004D, 5.000%, 12/01/13 - MBIA Insured   No Opt. Call    AAA      911,159 
1,385    Danbury, Connecticut, General Obligation Bonds, Series 2004, 5.000%, 8/01/14 - FGIC Insured   No Opt. Call    AAA      1,544,261 
    Hartford, Connecticut, General Obligation Bonds, Series 2005A:              
775    5.000%, 8/01/20 - FSA Insured   8/15 at 100.00    AAA      848,873 
525    4.375%, 8/01/24 - FSA Insured   8/15 at 100.00    AAA      534,293 
500    Hartford, Connecticut, General Obligation Bonds, Series 2005C, 5.000%, 9/01/17 - MBIA Insured   No Opt. Call    AAA      562,270 
400    Northern Mariana Islands, General Obligation Bonds, Series 2000A, 6.000%, 6/01/20 - ACA Insured   6/10 at 100.00    A      427,400 
1,500    Puerto Rico, General Obligation and Public Improvement Bonds, Series 2001A, 5.500%, 7/01/20 - MBIA   No Opt. Call    AAA      1,786,095 
    Insured              
    Regional School District 16, Beacon Falls and Prospect, Connecticut, General Obligation Bonds,              
    Series 2000:              
350    5.500%, 3/15/18 - FSA Insured   3/10 at 101.00    Aaa      384,524 
350    5.625%, 3/15/19 - FSA Insured   3/10 at 101.00    Aaa      386,351 
350    5.700%, 3/15/20 - FSA Insured   3/10 at 101.00    Aaa      387,058 
1,420    Regional School District 16, Connecticut, General Obligation Bonds, Series 2003, 5.000%, 3/15/16 -   3/13 at 101.00    Aaa      1,564,528 
    AMBAC Insured              
2,105    Stratford, Connecticut, General Obligation Bonds, Series 2002, 4.000%, 2/15/15 - FSA Insured   2/12 at 100.00    AAA      2,166,550 
1,000    Waterbury, Connecticut, General Obligation Bonds, Series 2004B, 5.000%, 4/01/13 - FSA Insured   No Opt. Call    AAA      1,101,220 
1,630    Westport, Connecticut, General Obligation Bonds, Series 2003, 4.750%, 2/01/19   2/12 at 100.00    Aaa      1,722,617 
    Tax Obligation/Limited - 13.6% (9.3% of Total Investments)              
2,000    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Child Care Facilities   7/09 at 102.00    AAA      2,192,960 
    Program, Series 1999C, 5.625%, 7/01/29 - AMBAC Insured              
    Connecticut, Special Tax Obligation Transportation Infrastructure Purpose Bonds, Series 2002B:              
2,000    5.000%, 12/01/20 - AMBAC Insured   12/12 at 100.00    AAA      2,167,880 
1,000    5.000%, 12/01/21 - AMBAC Insured   12/12 at 100.00    AAA      1,083,940 
500    Connecticut, Special Tax Obligation Transportation Infrastructure Purpose Bonds, Series 2003B,   1/14 at 100.00    AAA      538,230 
    5.000%, 1/01/23 - FGIC Insured              
625    Connecticut, Special Obligation Rate Reduction Bonds, Series 2004A, 5.000%, 6/30/11   No Opt. Call    AAA      682,838 
2,000    Puerto Rico Municipal Finance Agency, Series 2002A, 5.250%, 8/01/21 - FSA Insured   8/12 at 100.00    AAA      2,202,980 
1,000    Virgin Islands Public Finance Authority, Gross Receipts Taxes Loan Note, Series 1999A, 6.500%,   10/10 at 101.00    BBB      1,133,450 
    10/01/24              
1,000    Virgin Islands Public Finance Authority, Gross Receipts Taxes Loan Note, Series 2003, 5.250%,   10/14 at 100.00    AAA      1,120,670 
    10/01/19 - FSA Insured              
    Transportation - 1.0% (0.7% of Total Investments)              
750    Connecticut, General Airport Revenue Bonds, Bradley International Airport, Series 2001A, 5.125%,   4/11 at 101.00    AAA      784,380 
    10/01/26 (Alternative Minimum Tax)- FGIC Insured              
    U.S. Guaranteed *** - 20.2% (13.8% of Total Investments)              
1,500    Bridgeport, Connecticut, General Obligation Bonds, Series 2000A, 6.000%, 7/15/19 (Pre-refunded to   7/10 at 101.00    AAA      1,704,000 

      7/15/10) - FGIC Insured              
  935    Puerto Rico, The Children's Trust Fund, Tobacco Settlement Asset-Backed Bonds, Series 2000,   7/10 at 100.00    AAA        993,625 
      5.750%, 7/01/20 (Pre-refunded to 7/01/10)              
  40    Connecticut, General Obligation Bonds, Series 1993E, 6.000%, 3/15/12   No Opt. Call    AA***      46,170 
  2,000    Connecticut, General Obligation Bonds, Series 2002B, 5.500%, 6/15/21 (Pre-refunded to 6/15/12)   6/12 at 100.00    AA***      2,257,380 
  1,500    Connecticut, General Obligation Bonds, Series 2002A, 5.375%, 4/15/19 (Pre-refunded to 4/15/12)   4/12 at 100.00    AA***      1,678,335 
  2,525    Connecticut Health and Educational Facilities Authority, Revenue Bonds, Connecticut State   11/12 at 100.00    AAA      2,783,636 
      University System, Series 2003E, 5.000%, 11/01/15 (Pre-refunded to 11/01/12) - FGIC Insured              
  1,000    Connecticut, Special Tax Obligation Transportation Infrastructure Purpose Bonds, Series 2002A,   7/12 at 100.00    AAA      1,121,740 
      5.375%, 7/01/19 (Pre-refunded to 7/01/12) - FSA Insured              
  1,000    Connecticut, Special Assessment Revenue Bonds, Second Injury Fund, Series 2000A, 5.250%, 1/01/14   1/11 at 101.00    AAA      1,107,920 
      (Pre-refunded to 1/01/11) - FSA Insured              
  1,000    Connecticut, Clean Water Fund Revenue Bonds, Series 2001, 5.500%, 10/01/20 (Pre-refunded to   10/11 at 100.00    AAA      1,123,550 
      10/01/11)              
  1,000    Hartford, Connecticut, Parking System Revenue Bonds, Series 2000A, 6.400%, 7/01/20 (Pre-refunded   7/10 at 100.00    Baa2***      1,137,630 
      to 7/01/10)              
  300    Puerto Rico, General Obligation and Public Improvement Bonds, Series 2001, 5.125%, 7/01/30   7/11 at 100.00    AAA      330,411 
      (Pre-refunded to 7/01/11) - FSA Insured              
  1,000    Puerto Rico Infrastructure Financing Authority, Special Obligation Bonds, Series 2000A, 5.500%,   10/10 at 101.00    AAA      1,100,990 
      10/01/40              
  1,000    Waterbury, Connecticut, General Obligation Bonds, Series 2002A, 5.375%, 4/01/17 (Pre-refunded to   4/12 at 100.00    AAA      1,118,400 
      4/01/12) - FSA Insured              
      Utilities - 5.5% (3.8% of Total Investments)              
  1,575    Bristol Resource Recovery Facility Operating Committee, Connecticut, Solid Waste Revenue Bonds,   No Opt. Call    AAA      1,727,948 
      Covanta Bristol Inc., Series 2005, 5.000%, 7/01/12 - AMBAC Insured              
  1,000    Connecticut Development Authority, Pollution Control Revenue Refunding Bonds, Connecticut Light and   10/08 at 102.00    Baa1      1,087,320 
      Power Company, Series 1993A, 5.850%, 9/01/28              
      Eastern Connecticut Resource Recovery Authority, Solid Waste Revenue Bonds, Wheelabrator Lisbon              
      Project, Series 1993A:              
  395    5.500%, 1/01/14 (Alternative Minimum Tax)   1/06 at 100.00    BBB      399,385 
  1,290    5.500%, 1/01/20 (Alternative Minimum Tax)   1/06 at 100.00    BBB      1,292,580 
      Water and Sewer - 14.5% (9.9% of Total Investments)              
  1,185    Connecticut, State Revolving Fund General Revenue Bonds, Series 2003A, 5.000%, 10/01/16   10/13 at 100.00    AAA      1,300,419 
  1,500    Connecticut, State Revolving Fund General Revenue Bonds, Series 2003B, 5.000%, 10/01/12   No Opt. Call    AAA      1,655,865 
  2,550    Connecticut Development Authority, Water Facilities Revenue Bonds, Bridgeport Hydraulic Company,   9/06 at 102.00    AAA      2,671,074 
      Series 1996, 6.000%, 9/01/36 (Alternative Minimum Tax) - AMBAC Insured              
      Greater New Haven Water Pollution Control Authority, Connecticut, Regional Wastewater System              
      Revenue Bonds, Series 2005A:              
  900    5.000%, 11/15/16 - MBIA Insured   11/15 at 100.00    AAA      1,000,674 
  570    5.000%, 11/15/30 - MBIA Insured   11/15 at 100.00    AAA      614,124 
  760    5.000%, 11/15/35 - MBIA Insured   11/15 at 100.00    AAA      816,202 
      South Central Connecticut Regional Water Authority, Water System Revenue Bonds, Eighteenth Series              
      2003 A:              
  1,000    5.000%, 8/01/20 - MBIA Insured   8/13 at 100.00    AAA      1,087,120 
  1,525    5.000%, 8/01/33 - MBIA Insured   8/13 at 100.00    AAA      1,623,835 
  1,000    Stamford, Connecticut, Water Pollution Control System and Facility Revenue Bonds, Series 2003A,   11/13 at 100.00    AA+      1,060,325 
      5.000%, 11/15/32              
$   110,540    Total Long-Term Investments (cost $113,136,268) - 146.1%             119,214,803 

Other Assets Less Liabilities - 0.8%         $ 685,612  
Preferred Shares, at Liquidation Value - (46.9)%      (38,300,000)  
Net Assets Applicable to Common Shares - 100%        $ 81,600,415  

(1 )    All percentages shown in the Portfolio of Investments are based on net assets applicable to Common shares 
    unless otherwise noted. 
*     Optional Call Provisions: Dates (month and year) and prices of the earliest optional call or redemption. There 
    may be other call provisions at varying prices at later dates. 
**     Ratings: Using the higher of Standard & Poor's or Moody's rating. 
***     Securities are backed by an escrow or trust containing sufficient U.S. Government or U.S. Government agency 
    securities which ensures the timely payment of principal and interest. Such securities are normally considered 
    to be equivalent to AAA rated securities. 
N/R     Investment is not rated. 

Income Tax Information

The following information is presented on an income tax basis. Differences between amounts for financial statement
and federal income tax purposes are primarily due to timing differences in recognizing income on taxable market
discount securities and timing differences in recognizing certain gains and losses on investment transactions.

At August 31, 2005, the cost of investments was $113,119,711.

Gross unrealized appreciation and gross unrealized depreciation of investments at August 31, 2005, were as follows:

Gross unrealized:       
   Appreciation    $   6,163,145  
   Depreciation      (68,053 ) 
 
Net unrealized appreciation of investments    $   6,095,092  

Item 2. Controls and Procedures.

  1. The registrant's principal executive and principal financial officers, or persons performing similar functions, have concluded that the registrant's disclosure controls and procedures (as defined in Rule 30a-3(c) under the Investment Company Act of 1940, as amended (the "1940 Act") (17 CFR 270.30a-3(c))) are effective, as of a date within 90 days of the filing date of this report that includes the disclosure required by this paragraph, based on their evaluation of the controls and procedures required by Rule 30a-3(b) under the 1940 Act (17 CFR 270.30a-3(b)) and Rule 13a-15(b) or 15d-15(b) under the Securities Exchange Act of 1934 (17 CFR 240.13a-15(b) or 240.15d-15(b)).
  2. There were no changes in the registrant's internal control over financial reporting (as defined in Rule 30a-3(d) under the 1940 Act (17 CFR 270.30a-3(d)) that occurred during the registrant's last fiscal quarter that have materially affected, or are reasonably likely to materially affect, the registrant's internal control over financial reporting.

Item 3. Exhibits.

File as exhibits as part of this Form a separate certification for each principal executive officer and principal financial officer of the registrant as required by Rule 30a-2(a) under the 1940 Act (17 CFR 270.30a-2(a)), exactly as set forth below: EX-99 CERT Attached hereto.


SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

(Registrant)         Nuveen Connecticut Premium Income Municipal Fund        

By (Signature and Title)*          /s/ Jessica R. Droeger--Vice President and Secretary        

Date         10/28/05        

Pursuant to the requirements of the Securities Exchange Act of 1934 and the Investment Company Act of 1940, this report has been signed below by the following persons on behalf of the registrant and in the capacities and on the dates indicated.

By (Signature and Title)*         /s/ Gifford R. Zimmerman--Chief Administrative Officer (principal executive officer)        

Date         10/28/05        

By (Signature and Title)*         /s/ Stephen D. Foy--Vice President and Controller (principal financial officer)        

Date         10/28/05        

* Print the name and title of each signing officer under his or her signature.