According to this article, leaders of the New York legislature have expressed opposition to changing the September primary date for non-federal primary elections. Yet the New York City Board of Elections says a September primary for Mayor this year will cause great problems, because there isn’t enough time for a September primary and then a run-off primary.
According to Michael Drucker’s The Independent View, the State Board of Elections is now thinking seriously about using Instant-Runoff Voting for New York city mayoral primaries. The law requires a run-off primary if no one gets at least 40% of the vote in the primary itself.