N.H. Rev. Stat. § 42:3
Any person elected to an office where no other person was a candidate on the ballot for that office and no write-in candidate received 5 percent or more of the votes cast for that office, may be sworn in after the results are declared from the election and the annual business meeting has ended or at any time thereafter provided the oath is taken by the deadline established by RSA 42:6. If no recount of the office is requested, any person elected to an office that was contested or for which a write-in candidate received 5 percent or more of the votes cast may be sworn in upon the expiration of the period for requesting a recount provided in RSA 669:30.
RSA 42:3
RS 35:3. CS 37:3. GS 38:3. GL 41:3. PS 44:3. PL 48 :3. RL 60:3. 1994, 70:2. 2008, 280 : 1 , eff. Aug. 26, 2008.