N.J. Stat. § 40:45-19
In any regular municipal election held under section 14 of P.L. 1981, c.379 (C.40:45-18), if a sufficient number of candidates do not receive a majority of the votes cast to elect the required number of councilmen-at-large (or commissioners, or village trustees) or no candidate for mayor or no candidate for ward councilman receives a majority of the votes cast for his respective office, a run-off election in the municipality or ward, as the case may be, shall be held on the fourth Tuesday next following that municipal election; unless in any year that Tuesday shall be the date upon which a primary election shall be held, in which case the run-off election shall be held on the fifth Tuesday next following the municipal election. Alternatively, the run-off election shall be held at a special election on the subsequent Tuesday next after the first Monday in December in the case of a regular municipal election occurring on the day of the general election in November pursuant to subsection a. of section 1 of P.L. 2009, c. 196(C.40:45-7.1).
At the run-off election, the candidates for councilman-at-large (or commissioner, or village trustee) shall be those candidates not elected at the regular municipal election who received the greatest number of votes at that election, but the candidates shall be equal in number to twice the number of councilmen-at-large (or commissioners, or village trustees) remaining to be elected. The candidates for mayor or ward councilmen at the run-off election shall be the two candidates for the office who received the greatest number of votes at the regular municipal election. Military service ballots shall be printed and distributed for the run-off election in the same manner, so far as possible, as for other municipal elections.
The candidate or candidates who receive the greatest number of votes at the run-off election shall be elected to the office or offices to be filled. If two or more candidates shall be equal and greatest in votes for any of the purposes of this section, they shall draw lots to determine which one shall enter the run-off election, or be elected, as the case may be.
If any candidate to be voted for at the run-off election dies seven or more days prior to the run-off election, the candidate for the office not theretofore included in the run-off election, but next highest in number of votes for that purpose shall be substituted at the run-off election in the place of the deceased candidate and his name shall be substituted on the ballots for that of the deceased candidate.
N.J.S. § 40:45-19