I highly doubt it, but the DEC regulation maps do show cottontail, squirrel, and pheasant as open in the 5 boroughs. All other species are shown as "Closed".
But then, what can you hunt with in NYC? Can't use any firearms, or crossbow, or air rifle... Maybe a slingshot? wait, I think they might be illegal too... Can't remember right now... Maybe your bow? But is there any laws against discharging your bow on your own property? I dont think there is, hummm. Well, what ever.
So go figure...