N.H. Rev. Stat. § 48-A:12
An ordinance, code or bylaw adopted pursuant to the authority of this chapter may provide that any dwelling, building or structure situated within an historic district that is established under RSA 31:89-b, or within such other classes of dwellings, building or structure as the governing body shall determine to have special significance to the public interest and shall expressly define in such ordinance, code or bylaw, may be approved by the board of aldermen as a special exception, after public hearing, and the provisions of such ordinance, code or bylaw may be waived in their application to such dwelling, building or structure, in whole or in part or otherwise so modified as the housing board of appeals may determine.
RSA 48-A:12
1959, 293:1. 1965, 341:3, eff. Aug. 7, 1965.