UNITED STATES
SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE 14A

Proxy Statement Pursuant to Section 14(a) of the Securities
Exchange Act of 1934 (Amendment No.    )

Filed by the Registrant þ
Filed by a Party other than the Registrant o

Check the appropriate box:

o Preliminary Proxy Statement.

o CONFIDENTIAL, FOR USE OF THE COMMISSION ONLY (AS PERMITTED BY RULE 14a-6(e)(2)).

o Definitive Proxy Statement.

þ Definitive Additional Materials.

o Soliciting Material Pursuant to Section 240.14A-11(c) or Section 240.14a-12

NUVEEN CONNECTICUT PREMIUM INCOME MUNICIPAL FUND (NTC)

(Name of Registrant as Specified In Its Charter)

(Name of Person(s) Filing Proxy Statement if other than the Registrant)

Payment of Filing Fee (check the appropriate box):

þ No fee required.

o Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.

1) Title of each class of securities to which transaction applies:

2) Aggregate number of securities to which transaction applies:

3) Per unit price or other underlying value of transaction computed pursuant to Exchange Act Rule 0-11 (set forth the amount on which the filing fee is calculated and state how it was determined):

4) Proposed maximum aggregate value of transaction:

5) Total fee paid:

o Fee paid previously with preliminary materials.

o Check box if any part of the fee is offset as provided by Exchange Act Rule 0-11(a)(2) and identify the filing for which the offsetting fee was paid previously. Identify the previous filing by registration statement number, or the Form or Schedule and the date of its filing.

1) Amount Previously Paid:

2) Form, Schedule or Registration Statement No.:

3) Filing Party:

4) Date Filed:

Nuveen Funds
333 West Wacker Drive
Chicago, Illinois 60606

ANNUAL MEETING OF SHAREHOLDERS ADJOURNED

Dear Shareholder:

We recently distributed proxy materials regarding the Annual Meeting of Shareholders of the Nuveen Funds originally held on Tuesday, November 18, 2008 and subsequently adjourned to January 13, 2009. Our current records indicate that we have not yet received your voting instructions. The meeting has been adjourned again and will reconvene Tuesday, March 17, 2009 at 10:00 a.m. Central time, in the offices of Nuveen Investments, 333 West Wacker Drive, Chicago, IL.

Shareholders are being asked to consider several important proposals as more fully described in the materials sent to you. Those materials contain important information regarding the proposals that shareholders are being asked to consider. Please read the materials carefully.

Your Fund’s Board recommends shareholders vote “FOR” each of the proposals.

If you have any questions regarding the proposals, please call Computershare Fund Services, your Fund’s proxy agent, at 1-866-864-0471. Representatives are available Monday through Friday between the hours of 9:00 a.m. and 11:00 p.m. and Saturday from 12:00 p.m. to 6:00 p.m., Eastern Standard Time.

We urge you to act promptly to reduce the need for additional solicitation efforts or costly Meeting adjournments.

3 EASY WAYS TO VOTE YOUR PROXY:

1)	Automated Touch Tone Voting: Call the toll-free number listed on your proxy ballot and follow the recorded instructions.
2)	Log on to the Internet address on your proxy ballot and follow the instructions.
3)	Sign, date and return the enclosed proxy ballot using the enclosed postage-paid envelope.

Thank you for your prompt attention to this matter. If you have already voted, we appreciate your participation.

YOUR VOTE IS IMPORTANT!            PLEASE VOTE TODAY!

31709_ADJ