N.H. Rev. Stat. § 5-C:91

I. If it becomes known to the clerk of the town or city who has issued a marriage license that false information was given on the worksheet and included on the license, or if the clerk discovers information that is known to be incorrect because of inconsistencies with other records, the clerk shall notify the bride and groom and, if appropriate, the officiant, by certified mail of the inconsistency and request that they respond in writing within 30 days. The clerk shall also request that they attach to the response letter any information which will assist in correcting the worksheet information; send a copy of the letter to the division; and prepare the appropriate form under RSA 5-C:85 to correct the vital record. II. Upon receipt of a response letter under paragraph I, the division shall correct the marriage certificate in accordance with RSA 5-C:92. III. If no response is received, the division shall make a notation on the marriage certificate that there is conflicting information that has not been resolved or, in response to alleged bigamy or falsification of information provided on the marriage worksheet, pursue penalties in accordance with RSA 5-C:14.