N.H. Rev. Stat. Ann. § 45:13

The board of aldermen where the city government is composed of 2 bodies, or the city council where the city government is composed of one body, may choose one of their members to be chairman, and, whenever the mayor of any city shall be absent or shall be disabled by sickness or otherwise, he shall have all of the powers and perform all of the duties of the mayor during his absence or disability.