2006 New York Code - Acting Mayor.

 
    § 51. Acting mayor. Whenever there shall be a vacancy in the office of
  mayor,  or  whenever  by reason of sickness or absence from the city the
  mayor shall be prevented from attending to the duties of the office, the
  president of the common council shall act as mayor and possess  all  the
  rights  of mayor during such period of disability or absence. In case of
  a vacancy in the office of mayor he shall so act until noon of the first
  day of January  next  succeeding  the  election  at  which  the  mayor's
  successor  shall  be chosen. It shall not be lawful for the president of
  the common council when acting as mayor in consequence of the absence or
  sickness of the mayor to exercise any power of  appointment  or  removal
  from  office  unless such sickness or absence shall have continued for a
  period of thirty days; or to sign, approve or disapprove  any  ordinance
  or resolution unless such sickness or absence shall have continued for a
  period of at least nine days.