In NY, you can use a bow or muzzleloader during the regular (shotgun, in my region) season, but if you take a deer you have to use the REGULAR tag (or DMP tag if you have one), not your bow or muzzleloader tag.

Just to play devil's advocate, I grew up hunting PA and I know how the hunting season is there (especially on public land), BUT most of these gun hunters take their gun and go out for one or two weekends A YEAR to hunt. They don't know the first thing about bow hunting. I am sure if you asked a lot of gun hunters, they would assume that if you shoot a deer with a bow, it drops just like it does for a gun. It would not surprise me if a deer ran down to a guy (especially if he didn't hear a shot) and he shot it again. That still doesn't excuse him from notrelenting after you reason with him (and show him the hole.) Just a different perspective on it.