Conn. Gen. Stat. § 54-240f: Confidentiality of marriage records.

A program participant may request that the participant's marriage records be kept confidential by appearing in person with the participant's spouse or intended spouse before the authorized personnel for the office of the registrar of vital statistics in the municipality where the marriage was or is to be celebrated and presenting the participant's certification card to such personnel. Upon such request, such registrar shall keep the participant's marriage records confidential and shall not make available for inspection or copying the name and address of a program participant or of the participant's spouse or intended spouse contained in the participant's marriage records, except (1) if requested by a law enforcement agency, to the law enforcement agency, (2) if directed by a court order, to a person identified in such order, or (3) if notified by the Secretary of the State that the program participant's certification has been cancelled.