N.H. Rev. Stat. Ann. § 659:49-b

The moderator or the moderator's designee may authorize the opening of absentee ballot outer envelopes on election day prior to the time established for processing absentee ballots in RSA 659:49, provided that the opening of the outer envelopes occurs in public with notice of the time and place. The envelope containing the ballot shall not be removed from the outer envelope at such time, and the outer envelope containing the inner envelope shall be secured until it is processed pursuant to RSA 659:50.