N.H. Rev. Stat. Ann. § 46:4

The mayor, aldermen and common council shall meet in convention, on such day as shall be appointed by law or ordinance, at 10 o'clock in the forenoon, when the oath of office may be administered to the mayor-elect, if present, by any judge or justice of the peace, and to the aldermen and common councilmen by the mayor or any justice of the peace.