N.H. Rev. Stat. Ann. § 42:4

The town clerk shall immediately, or in accordance with the time adopted by the governing body, if one has been adopted, direct a constable or police officer to notify the persons so chosen or notify such persons by registered mail, return receipt requested, to appear before the clerk within 6 days after receiving the notice, and take the oath by law prescribed. The officer shall, within 4 days, give personal notice to the persons therein named, or leave a notice in writing at the abode of each, and make return of the precept and of his doings therein to the town clerk within 6 days.