§ § 6-162Primary; New York City, run-off

when no candidate for the office of mayor, public advocate or
comptroller receives forty percent or more of the votes cast by the
members of a political party for such office in a city-wide primary
election, the board of elections of such city shall conduct a run-off
primary election between the two candidates receiving the greatest
number of votes for the same office.

2. In any jurisdiction that authorizes a run-off election after a
primary election, if one of the two candidates receiving the greatest
number of votes for the same office files with the local board of
elections a certificate of withdrawal within three days following such
primary election, the board shall accept and certify the withdrawal and
declare the remaining candidate the winner and no such run-off primary
election shall be held. Such certificate of withdrawal shall be in
affidavit or affirmation form as determined by the state board of
elections.