N.Y. Second Class Cities Law § 51

§ 51. Acting mayor. Whenever there shall be a vacancy in the office of\nmayor, or whenever by reason of sickness or absence from the city the\nmayor shall be prevented from attending to the duties of the office, the\npresident of the common council shall act as mayor and possess all the\nrights of mayor during such period of disability or absence. In case of\na vacancy in the office of mayor he shall so act until noon of the first\nday of January next succeeding the election at which the mayor's\nsuccessor shall be chosen. It shall not be lawful for the president of\nthe common council when acting as mayor in consequence of the absence or\nsickness of the mayor to exercise any power of appointment or removal\nfrom office unless such sickness or absence shall have continued for a\nperiod of thirty days; or to sign, approve or disapprove any ordinance\nor resolution unless such sickness or absence shall have continued for a\nperiod of at least nine days.\n