N.H. Rev. Stat. § 5-C:85

Except for divorce records which are amended by the court, 2 forms shall be used to correct any vital record which contains inaccurate, erroneous, or missing information. I. The first form shall be used if corrections to a vital record are to be made within 6 months of the filing of the birth, marriage, or death, except that the form shall not be used for the addition of a husband's name to the birth record. The form shall be completed by the clerk of the town or city with the following: an indication of the type of vital record, whether the correction is being done in order to enact a legal change of name, correct a state or town record which contains incorrect information, or make a correction due to spelling or other typographical errors; the items to be corrected; the items as they now appear on the record; the items as they should appear on the record after the correction is made; the date of the vital record event; information sufficient to identify the person requesting the correction; the source for the correction; the date the original vital record was filed with the clerk of the town or city; and the clerk's signature, town or city name, and date the clerk of the town or city signed the form. The form shall be forwarded to the division upon completion in order to have the correction made to the state record. II. A second form shall be used if corrections to a vital record are to be made more than 6 months after the filing of the birth, marriage, or death. The form shall be completed by the clerk of the town or city with the following: an indication of the type of vital record; the items to be corrected; the items as they now appear on the record; the items as they should appear on the record after the correction is made; the date of the vital record event; the name and address of the person requesting the correction; the birthplace of the person requesting the correction; a list of evidence presented indicating the type of documentation presented by the requestor; and the signature of the clerk of the town or city and date signed by month, day, and year. The form shall be signed by the person requesting the correction and shall be notarized by a notary public or justice of the peace. The clerk of the town or city shall submit the form to the state registrar along with a copy of the supporting documentation. The state registrar shall review the documentation for completeness and indicate approval or disapproval of the requested changes in accordance with RSA 5-C:40 for birth records, RSA 5-C:54 for marriage records, and RSA 5-C:94 for death records. If the registrar approves the change, the registrar shall correct the record and return the approved form to the clerk of the town or city.