A person born in the State may file or amend a certificate after the time prescribed, upon submitting proof as required by rules adopted by the department of health. Certificates registered after the time prescribed for filing by the rules of the department of health shall be registered subject to any evidentiary requirements that the department adopts by rule to substantiate the alleged facts of birth. The department may amend a birth certificate to change or establish the identity of a registrant’s parent only pursuant to a court order from a court of appropriate jurisdiction or pursuant to a legal establishment of parenthood pursuant to chapter 584. Amendments that change or establish the identity of a registrant’s parent that are made in accordance with this section shall not be considered corrections of personal records pursuant to chapter 92F.