Conn. Gen. Stat. § 7-57

(b) If the department denies the request for a delayed registration of birth, such adult, parent or legal guardian may petition the court of probate for the district where such birth occurred for an order requiring the department to prepare a certificate of birth of such adult or such minor. The petitioner shall include with the petition the affidavits and other documentary evidence submitted to the department in accordance with subsection (a) of this section. Such court shall schedule a hearing and cause notice of the hearing to be given to the following persons: (1) The petitioner; (2) if the delayed registration of birth is sought for a minor, (A) the parent or legal guardian of the minor, and (B) if the minor is twelve years of age or older, the minor; (3) the commissioner; and (4) any such other person as the court may determine has an interest in the hearing. The commissioner or the commissioner's authorized representative may appear and testify at such hearing. The petitioner shall have the burden of proving the facts of the birth. If the court finds by a preponderance of the evidence that the birth occurred on the date and at the place alleged by the petitioner, the court shall issue an order containing the person's name, sex, date of birth, place of birth and any other identifying information as the court deems appropriate and directing the department to issue a delayed birth certificate. Upon receipt of a certified copy of any such order, the department shall prepare a birth certificate based on the facts set forth in the court's order and transmit a copy of the certificate to the registrar of the town where the birth occurred and to the registrar of the town where the mother resided at the time of birth.

(c) In any proceeding under subsection (b) of this section, the court, on the motion of any party or on the court's own motion, may order genetic tests, which shall mean deoxyribonucleic acid tests, to be performed by a hospital, accredited laboratory, qualified physician or other qualified person designated by the court to determine parentage. The petitioner shall be responsible for the cost of any genetic test required by the court, except the department shall pay such cost for any petitioner who is found by the court to be indigent. If the results of such test indicate a ninety-nine per cent or greater probability that a person is the mother or father of the adult or minor for whom a delayed registration of birth is sought, the results shall constitute a rebuttable presumption that the person is, in fact, the mother or father of the adult or minor for whom a delayed registration of birth is sought.

(d) Birth certificates registered one year or more after the date of birth shall be marked “delayed” and indicate (1) the date of the delayed registration, (2) the person's name, sex, date of birth, place of birth and any other identifying information prescribed by the commissioner, as such facts of the birth have been determined based upon the evidence presented to the department or stated in a court order, as the case may be, and (3) when the facts of the birth are determined by court order, a statement that the birth is registered pursuant to court order.