Conn. Gen. Stat. § 5-158a: Part A and B members may elect to participate in part A and Social Security.

Each state employee who is a member of the state employees retirement system, part A, or who is a member of the state employees retirement system, part B, or who becomes a member of either of the above systems, shall be eligible, as provided in subsection (a) of section 5-158b, to contribute and be a member of part A and participate in Social Security without diminution of his state retirement salary; provided such state employees, who are members of part A, as provided for, or as may be provided for, by federal-enabling legislation, may elect to join the Social Security System.