Conn. Gen. Stat. § 7-451: Retroactive coverage.

Any agreement or modification entered into under sections 7-452 to 7-455, inclusive, to cover services of employees of municipalities in positions covered by the fund may be made retroactive to the extent permitted by Section 218(f) of the Social Security Act, but not prior to January 1, 1956. Any contributions payable by such a municipality or by the employees of such a municipality for such retroactive coverage shall be paid from the fund. The commission shall adjust the prior service contributions by such municipalities to reflect over the remainder of the amortization period the municipality's share of the cost of such retroactive coverage.