N.H. Rev. Stat. § 5-C:56

I. Pursuant to RSA 458:1, a marriage certificate shall be voided if an individual accused of bigamy fails to respond to a certified letter or a founded claim of bigamy has been referred to the county attorney by the state registrar as provided in RSA 5-C:55. II. If the marriage certificate has already been filed with the division, the state registrar shall mark the record "VOID" on the face of the marriage certificate. If the charge of bigamy has been substantiated, the appropriate form as described in RSA 5-C:85 shall be returned by the state registrar to the clerk of the town or city. If a copy of the marriage certificate is also on file at the clerk's office, the clerk shall make a notation to the face of the local record indicating the marriage certificate has been declared "VOID" by the state registrar and the date. III. A copy of the document that voided the previous marriage certificate shall be presented to the clerk of the town or city in the event that either of the parties wishes to marry in the future and he or she completes a new marriage license in the state of New Hampshire. The new marriage license shall not make reference to the voided marriage certificate.