N.H. Rev. Stat. Ann. § 41:48

Any permanent constable or police officer who is either elected under the provisions of RSA 41:47 or appointed for full-time duty under the provisions of RSA 105:1, and who is in compliance with the requirements of RSA 106-L:6, shall continue to hold such office during good behavior, unless sooner removed for cause by the selectmen, after notice and hearing, or unless the town has rescinded its action as provided in RSA 41:47. Any such elected permanent constable or police officer shall be deemed to be a permanent policeman, and entitled to benefits under the provisions of RSA 103 if otherwise qualified.