N.H. Rev. Stat. § 659:59
The moderator may order the assistant moderator in writing to process absentee ballots and to count the votes cast at the additional polling place in the presence of and with the assistance of the assistant town clerk and election officials in the manner prescribed by this chapter. After the processing of absentee ballots and the counting are complete, the assistant moderator shall place the counted ballots in the ballot box and shall seal it, and the assistant town clerk shall certify the same. The assistant moderator shall also seal in a package the duplicate checklists used at the additional polling place together with the absentee envelopes and the spoiled and unused ballots; and he, together with the assistant town clerk, shall immediately deliver the ballot box, checklists, absentee envelopes, unused and spoiled ballots, and a written report of his count signed by him and the assistant town clerk to the moderator of the town at the central polling place. If the moderator does not order the counting as provided herein, the assistant moderator shall comply with the provisions of RSA659:62.
RSA 659:59
1979, 436:1. 1981, 454:7, eff. Aug. 22, 1981.