Conn. Gen. Stat. § 46b-35a: Refusal to provide services or accommodations related to the solemnization or celebration of a marriage on religious grounds.

Notwithstanding any other provision of law, a religious organization, association or society, or any nonprofit institution or organization operated, supervised or controlled by or in conjunction with a religious organization, association or society, shall not be required to provide services, accommodations, advantages, facilities, goods or privileges to an individual if the request for such services, accommodations, advantages, facilities, goods or privileges is related to the solemnization of a marriage or celebration of a marriage and such solemnization or celebration is in violation of their religious beliefs and faith. Any refusal to provide services, accommodations, advantages, facilities, goods or privileges in accordance with this section shall not create any civil claim or cause of action, or result in any state action to penalize or withhold benefits from such religious organization, association or society, or any nonprofit institution or organization operated, supervised or controlled by or in conjunction with a religious organization, association or society.