Legality of shooting in the backyard

Hey all,

I live in suburban New Jersey. I looked at the laws and local ordinances and I believe it's legal to shoot in my backyard. The crossbows are not illegal and not a firearm so it doesn't violate discharge laws as far as I can see. I set up a range with safety in mind and all that. BUT it is certainly not the norm where I live and my neighbors may freak out. I'd like to be certain I am safe and legal. Any advice or experience with this?