As far as I'm aware, if an animal you've wounded crosses a property line onto property that you're not given express permission to be on in the USA, you can not follow it, nor shoot across the property line. That's illegal pretty much everywhere. The best approach is not to hunt near a property line. If it does happen, I would guess it's up to the property owner where the animal dies, whether you're going to get that animal or not - unless you just go and take it without being caught. If you're hunting a property it is probably a very good idea to talk to neighboring property owners and ask about that exact scenario *before* it happens. Most will probably be fine with you taking the animal as long as they're aware it might happen. Not so much if you cross onto their property without permission. Just depends on the neighbor I suppose.
I recently had a situation that dealt with similar property issues. I have a couple acre yard right in the middle of the city and in the far back I've got a nice 40 foot border of wild wooded area on 3 sides that acts as a sort of natural privacy fence. It's about like having a little meadow in the middle of a forest. I walk the fence line every spring to check for damaged trees or garbage, etc.
This year I find a 12-15 foot wide section all along my property line with the brush cleared to the ground, 3 or 4 trees cut completely down and several of my 80 year old 75 foot tall pines with all the branches cut completely back to the trunk on one side, 12-15 feet away from the fence on my side. Needless to say, I was pissed. The public utility owns the property on the other side of the fence and they had some tree service butcher my property (400 feet back from any road - no power lines, no easement, etc.) without permission. I called and they said "oh that wasn't us, we have contractors" like that makes any difference. They told me that some trees fell on the fence. Except they cut down 3 or 4 trees and butchered a bunch of others. Also, I walk that property line every year and not one time has a tree fallen on that fence in 20 years, now all of a sudden there were 3 or 4? And the fence is not damaged one bit. I think they're full of shit and they just didn't want to trim branches or who knows what.
I said, "how do I know that a tree fell on the fence, do you have evidence of that? And what were you doing on my property without getting permission? If there was damage, you have a responsibility to show me first and ask permission before you come onto my property, and certainly not do the rest of the butchering that you did." I kept that buffer zone so I didn't have to look at their ugly fence in my backyard, now it's very visible. Not happy, may go to small claims if they don't take some responsibility.
Out in the red states, that sort of behavior causes retaliation!
