Really don't have to go in at all. I remember testifying for this bill and didn't think it would actually pass, but it did!!
This is from the state:
Pistol Permit Renewals
Ninety (90) days prior to the expiration of your permit, the issuing authority will mail out a renewal letter to your last known address. The law requires that you notify the issuing authority within 48 hours of changing your address. Upon receipt of the renewal letter you can proceed to either the Special Licensing and Firearms Unit (SLFU) main office at State Police Headquarters, 1111 Country Club Road, Middletown, CT or the satellite location set up at Troop G in Bridgeport to process your renewal. Effective October 1, 2011 per Public Act 11-186 you may also mail in your renewals. Instructions for renewal by mail can be obtained in the link below. If you appear in person an updated photo and your signature will be collected. You are required to bring positive photo identification with you. Directions to these facilities and business hours are posted below. The cost of renewing a state pistol permit is $70.00 payable to the Treasuer, State of Connecticut in the form of a check or money order. Applicants must provide that they are legally and lawfully in the United States, such as a birth certificate, U.S. Passport or Naturalization papers. Legal Alien Residents must provide Alien Registration numbers and 90-day proof of residency. Please use link for additional instructions: DPS-769-C Instructions to Applicants & Photo Pistol Permit Schedule