N.H. Rev. Stat. § 21:32

I. By the words "publish," "published," "publishing," or "publication," when notice is required or permitted to be given by publication, shall be intended publication in a newspaper circulated in the vicinity, and the publication shall be for 3 weeks successively, and the last publication one week, at least, before the day or thing of which notice is given, unless otherwise specially provided. II. The terms "publication of daily statewide circulation," "publication of general statewide circulation," or "publication in a newspaper of statewide circulation" regarding any requirement of any executive branch state agency, board, department, or official to provide notice under state law in respect to any real or personal property, act, event, hearing, or other occurrence, by advertisement or notice, shall mean publication of such notice at the offices of the agency, board, department, or official; prominently on a publicly accessible Internet site maintained by the agency, board, department, or official; and in any local or regional publication circulated where the real or personal property is located or where the act, event, hearing, or other occurrence is to take place, all in accordance with the time frame for notice prescribed by law.