Conn. Gen. Stat. § 38a-624a
The marriage laws of this state shall not be construed to affect the ability of a fraternal benefit society to determine the admission of members as provided in section 38a-598 or to determine the scope of beneficiaries in accordance with section 38a-636, and shall not require a fraternal benefit society that has been established and is operating for charitable and educational purposes and which is operated, supervised or controlled by or in connection with a religious organization to provide insurance benefits to any person if to do so would violate the fraternal benefit society's free exercise of religion as guaranteed by the first amendment to the Constitution of the United States and section 3 of article first of the Constitution of the state.
Conn. Gen. Stat. § 38a-624a
( P.A. 09-13, S. 18.)