N.H. Rev. Stat. § 231:167
If any person shall be damaged in his estate by the erection of any such poles or other structures, or by the installation of any such underground conduits or cables or by installing or placing any wire, cable, guy, cross-arm, fixtures, transformers, manhole, drain, or other apparatus in or under the highway by authority of any such license, he may apply to the selectmen to assess his damages. Such proceedings shall thereupon be had as are provided in the case of assessment of damages in laying out highways by the selectmen, and such damages, if any, may be awarded as shall be legally and justly due.
RSA 231:167
1881, 54:6. PS 81:6. 1897, 81:1. PL 97 :6. 1935, 100:1. RL 113:8. 1945, 188:1, part 24:8. RSA 254:9. 1981, 87:1, eff. April 20, 1981.