N.J. Stat. § 40A:16-14
If a governing body shall fail to fill a vacancy in the office of mayor as provided in N.J.S. 40A:16-4a or 40A:16-5a within the 30-day period prescribed by N.J.S. 40A:16-11 or 40A:16-12, the municipal clerk shall forthwith fix the date for a special election to fill the vacancy to be held not less than 45 days nor more than 50 days after the expiration of the time fixed for the filling of the vacancy. If the date fixed for a special election shall fall within 20 days prior to the holding of any general election, regular municipal election or any other election within the municipality, the vacancy shall be filled at that election. If the date fixed for a special election shall fall within 20 days after the holding of any general election, regular municipal election or any other election within the municipality, then the special election to fill the vacancy shall be held not less than 20 days nor more than 25 days from the date of that election.
Notwithstanding the foregoing, if a vacancy in the office of mayor occurs in the final 6 months of the term of the mayor, no special election shall be held to fill the vacancy.
No appointment shall be made by a governing body to fill a vacancy occurring in the office of a mayor after the fixing of a date for a special election to fill the vacancy pursuant to this section.
N.J.S. § 40A:16-14