Go ahead and shoot the deer. Do it in a legal manner and if it lands on your neighbors yard politly go over and ask them if you can retrieve it. Take your shot very early morning or late day so there is less chance of it even being seen….I think late day is better.
I am in a township so I don’t have to follow city ordinance. My lot is 1 acre and most of my neighbors lots are just slightly larger. We have a bike trail that divides my lot so I also own a seperate .24 acre lot on the other side of this trail. I have taken a deer in this area with a heart shot at close range, it went only 20-30 yards and died in a dry creek bed. I went to the my neighbors house and asked him if I could get the deer and he said sure go ahead. There was no problem and this was a neighbor who I had actually only talked to one time before this….and that was to ask him to take down the barbed wire he had strung onto my property. I should point out that the deer ended up in a spot where no one was going to see it about 150 feet from their house, lots of trees in the way and down a hill but the odds of that happening in this area are pretty good.
So I am in favor of you exercising your right to hunt but only you know the lay of the land you are working with. It might go well but it could also go poorly as others have pointed out. But I wonder what would happen if you shoot one and it ends up in a neighbors yard who says ‘no leave it.’ So the deer is just left to rot in their yard? Really, do they want that? That might happen but I doubt it. This is just my opinion and experience. I am sure others will say I am wrong. I also want to point out that I rarely hunt my own yard anymore. There are too many people out in their yards in the fall and too much movement so rarely have I ever had a deer in range and that is OK. Because of that I usually only go out very late in the season when it is snowing or a slight rain. Fortunatley, the last few years my son and I been able to get permission to hunt somewhere else and have taken a deer or two by mid-season so if I do go sit out back it is just to enjoy the snow falling and to watch for something to come by. I may have a bow in my hand but I really don’t need another deer.
Good luck with your decision.