Conn. Gen. Stat. § 7-58

Any American citizen who becomes the parent of a child or children born outside the United States, and who was a resident of this state at the time of leaving the United States, may file, with the town clerk of the town in which the parents reside or resided, a certified copy of the record of birth of such child or children issued to the parents by an official authorized to issue such records of birth at the place of birth. When such certified copy has been filed, copies of such record of birth may be issued by such town clerk in the manner prescribed by law.