I know they are legal to have my grandsponsor has one. She is an education bird though and wasnt for hunting but i cant see why it would be illegal to hunt with one as long as you hunt during legal hunting hours it should be fine.
If you are asking this question, you must not be familiar with the falconry regs of New York. Here is the link for them. www.dec.ny.gov/regs/3940.html#13314
Also the birds that can be held for education is no indication of what can be used for falconry.
And remember just because you can fly the species does not mean you can trap them in your state or any state. May only be able to get certain species by captive breeding only.