N.H. Rev. Stat. § 660:5
If directed by the secretary of state, the state police shall collect all ballots requested from the town or city clerks having custody of them and shall deliver them to the public facility designated by the secretary of state. At the time and place so appointed, the ballots cast for such office shall be counted by the secretary of state and such assistants as the secretary of state may require. When counting the ballots, the secretary of state or his or her assistants shall visually inspect each ballot. No mechanical, optical, or electronic device shall be used for the counting of ballots. The candidates, their counsel, and assistants shall have the right to inspect the ballots and participate in the recount under such suitable rules as the secretary of state may adopt. If the candidate requesting the recount cannot attend the recount, the candidate shall designate, in writing, to the secretary of state the name of an individual who will attend the recount and who will be authorized to make decisions on the candidate's behalf. Each candidate or his or her counsel or designee shall have the right to protest the counting of or failure to count any ballot. The secretary of state shall thereupon rule on said ballot and shall attach thereto a memorandum stating such ruling and the name of the candidate making the protest. If, at any time during the counting of the ballots, a discrepancy appears in any ballot for any reason, the secretary of state shall suspend the recount until the discrepancy is resolved, at which time the secretary of state shall continue the recount. In no event shall a discrepancy result in a second recount for the same candidate, as provided in RSA 660:3.
RSA 660:5
1979, 436:1. 1981, 510:4. 1983, 175:5. 2006, 41:1. 2007, 136:1, eff. Aug. 17, 2007.