It's really going to depend on the species. So you'll eventually going to have to find out, otherwise you'll have to do trial and error for tankmates. Some docile species (docile in regards to other crays, people, etc) will actively hunt fish even though they seemed mild in temperament (and vice versa, some aggressive species ignore fish all together).
Is it wild caught from your state? Because NY has the following species:
Cambarus bartonii bartonii - Stays relatively small. It's okay with fast moving, larger fish and most plants (I've kept these with plecos, barbs, silver dollars, etc... they're good at catching things like glofish, feeders, etc).
Cambarus robustus - Get's very large (adults found around 8-9in). It's a little awkward at catching fish, so something small, fast, etc would work with it.
Orconectes immunis - Semi-aggressive with most things, but very sluggish. Spends more time trying to burrow into sediment.
Orconectes limosus - Doesn't get very large (slightly larger than most dwarf crays), but it's very aggressive. Something bigger than it that could handle being nipped occassionally.
Orconectes obscurus - Average crayfish temperament, you could try fast moving fish or fish too large to be held onto.
Orconectes propinquus - Same as above.
Orconectes rusticus - Aggressive and large, will attack anything. Very good at catching things despite their size and bulk. Best not housed with fish.
Orconectes virilis - Large, but fairly docile. Aggression is usually seen only in the males (towards other males). I keep (and have kept for a long time) these with fish with no issues (bottom dwelling catfish, feeders, tetras, etc).
Procambarus acutus acutus - Aggressive, similar personality to P. alleni. Best not housed with any fish.
You can take these names and google them, it'll give you pictures and you can find out which species you have. If you're going to try housing crays and fish together, give both plenty of places to hide away from each other. And target feed the crayfish daily, so it's less inclined to scavenge and/or actively hunt. Or maybe just get pretty feeders or livebearers like rosies, guppies, endlers, etc ... so that if there's a loss, it's not a bad one. Good luck! ^_^
