N.H. Rev. Stat. Ann. § 45:9

He shall preside in the board of aldermen and in convention of city councils, and shall be ex-officio chairman of the board of overseers of the public welfare. He shall have a negative upon the action of the aldermen in laying out highways, and in all other matters; but shall have no vote except in case of an equal division; and no vote can be passed or appointment made by the board of aldermen over his veto unless by a vote of 2/3, at least, of all the aldermen elected.