Conn. Gen. Stat. § 46b-22b: Refusal to solemnize or participate in ceremony solemnizing a marriage on religious grounds.

(a) No member of the clergy authorized to join persons in marriage pursuant to section 46b-22 shall be required to solemnize any marriage in violation of his or her right to the free exercise of religion guaranteed by the first amendment to the United States Constitution or section 3 of article first of the Constitution of the state.

(b) No church or qualified church-controlled organization, as defined in 26 USC 3121, shall be required to participate in a ceremony solemnizing a marriage in violation of the religious beliefs of that church or qualified church-controlled organization.