Here in MO on the property I hunt, there are 5 neighbors. I always contact them by phone or stop by their house to check with them before the season to make sure I can access their property if a deer I shoot happens to make it's way onto their property. They always say yes, but I make sure I ask every year. This way, there are no surprises and they develop a sense of trust and respect for you since you are asking first instead of just GOING on their property.
I once went over to my sister's house and her neighbor was an avid hunter. In his back yard there was a large wooden swingset and hanging from this upside down was the largest buck I have ever seen. He was a 12 point and probably around 160-170 class. As I walked over to admire it, I retraced my steps when I saw the game warden pull up and knock on this neighbors front door. The neighboring property to where this guy hunts filed a complaint that this guy shot this deer on HIS property and retreived it by trespassing. Of course my sis's neighbor denied it. The game warden told him, "let's go out to your hunting spot, you show me where you shot him, if there's blood on your side of the fence, you can keep the deer, if there isn't any blood, then it's trouble". They went, and about 2 hours later I witnessed the game warden and another officer loading up the biggest deer I ever saw. and they handed the guy a ticket w/a fine. No blood on his side of the fence.
GENERALLY.... you can make a case for yourself if you shoot an animal and are trying to retreive it on a neighbors property, but you had better make sure you shot it on YOUR property and that there is clear evidence. If not, I would contact the neighbor first.