I don't think it's really legal in the US either. No matter what, how is the neighbor gonna complain? I can just imagine the complaint: "Yeah, my neighbor shot my dogs which happened to be on his property and happened to be eating his property". lol.
I have a neighbor living across the street with 2 dogs, 2 geese, and a number of ducks. This is IN Des Moines BTW. Anyway, their animals are always over my yard doing their duty or just being a nuisance.
One time one of their geese was in my yard foraging and the kids were afraid of it (they are kinda large after all). So I went out and tried to shoo it away. Man geese are stupid! I had to get a stick and beat it off my yard. I told the guy the next time I see any of his geese in the yard, I would be having a free Thanksgiving dinner.
Another time one of the dogs bit one of my stepkids while checking the mail (not enough to break the skin though). I went over there and told him if this happened again I was going to kill his dog right in front of him and then kick the sh!t out of him for just being a waste of flesh. Yeah, I was mad. In retrospect, I should have just called the cops. He didn't say anything, but they haven't bothered me badly since.
Every once in a while, one of the dogs looks like it wants to come over, but a sharply thrown rock dissuades them.
I don't blame the animals so much as the owners. If an animal causes damage or bodily harm, the OWNER should be put to sleep.