N.H. Rev. Stat. § 47:2
The city councils shall have the power to provide for the appointment or election of all necessary officers for the good government of the city not otherwise provided for, and to prescribe their duties and fix their compensation; but no person who is a member of the city councils shall be elected by the city councils or appointed by the mayor and aldermen to any office pertaining to elections, or where the remuneration of the office exceeds $100 in any one year. In case of the election or appointment of any member of the city councils to any office where the remuneration of the office does not exceed $100 in any one year, the member shall not be present or vote when the member's election or appointment is made.
RSA 47:2
1846, 384:21. 1855, 1699:20. GS 44:2. GL 48:2. PS 50:2. 1921, 100:1. PL 54 :2. RL 66:2. 1996, 268:2, eff. Aug. 9, 1996.