I live in NYC and candidates are often listed on multiple parties on the ballot. You’ll often see the Republican also listed as the Constitution party candidate and the Democrat listed as the Green party and Working Families party candidate for example.
Here’s what it says in Wikipedia:
Like other minor parties in New York, the Independence Party sometimes nominates its own candidates and sometimes endorses one of the major party candidates using electoral fusion. The listing of a major-party candidate on the Independence line can be seen as an indication of that candidate’s friendliness to centrist views.
Electoral fusion is an arrangement where two or more political parties on a ballot list the same candidate, pooling the votes for that candidate.
The entry from Wikipedia is a bit misleading.
New York State has a law referred to as Wilson-Pakula that is unique in the 50 states. It allows a candidate to run on the ballot of another party or parties if his original party and the other party or parties agree to it. He also runs on his own party’s line. (There was a similar law in Connecticut, but the candidate could only run on one party’s line.)
The stress in the Wikipedia article on the Independence Party is misleading because first of all it is an actual party, with that misleading name. If you want to be independent, you register as “unaffiliated.” No doubt someone from the Independence Party added that “information” to the Wikipedia article. (The Independence Party was sued over the use of that name, by the party whose place in the batting order was usurped by the IP. The IP won.)
So Crowley was going to run as both Democrat and Working Families. He is stuck on the Working Families Party line unless he is appointed to a judgeship, which would disqualify him, but the appointment would be in a district where he does not now live, so he doesn’t want to do that. The Dems stick together, and he will not try, or at least will try to appear not to try, to win without the Dems.
Although the district has gone very Latino, there is still a core of Irish and Italian voters from the old days, and this whole thing has gotten so much attention that it’s anybody’s guess what will happen.