RSA 45:6: Election to Fill.

As soon as may be after such vacancy shall occur, the board of aldermen and the common council shall meet and respectively declare the existence of such vacancy and the cause thereof, whereupon said board of aldermen and the common council shall meet in convention and elect a mayor, who shall serve until the next regular election and until his successor is duly elected and qualified. No person who is at the time of the occurring of the vacancy a member of either the board of aldermen or the common council shall be eligible to election by said convention.