They may be illegal in NY if the blades lock, from NYS DEC:



Barbed Broadheads
Barbed broadheads are illegal for hunting big game. A barbed broadhead is one in which the angle formed between the trailing or rear edge of any blade and the shaft is less than 90 degrees. Broadhead examples on the right compare one that is barbed to three that are legal. Broadheads with retractable blades are legal.