Nieghbor's dogs. The exact situations have happened to me more times over the years than I care to remember.
First off, I have lived in my current location for 30+ years, the property has been in my family for 80+ years. When I first moved onto my property it was rural, very rural, I had one nieghbor, and he wasn't even within eye sight. The road was a small gravel country lane, with the trees alongside shading the road. It was a favorite drop off point for every unwanted animal in the parish. Dogs, cats, puppies, kittens, sometimes momma and babies. At that time we had absolutely no animal control, none, not anyone. It was strictly old west, take care of justice yourself. The number of animals I had to put down still haunt me today.
For my livestock protection it was electric fence around everything, and a trusty Marlin 30/30. A 20 ga with rifled slugs does a good job too. 22 cal not much good for anything beyond coon and cat size.
Fast forward 10 years, 1985 or so, the area is beginning to develop. A few nieghbors within ear shot. The family across the road has divided their 40 acre tract into 1 acre lots. Now instead of drop offs, I got labs, german shepherds, terriers, of every description comming from all directions. Get up in the morning to find 10 or 12 dogs in the yard, no kidding 10 or 12. And, to put the icing on the cake, still no parish/municipal animal control.
At this time one particular dog, that I believe had a good share of the pitbull breed in him, penetrated the electric fence surrounding my chickens. Killed a wheelbarrow full in one night. I knew who the dog belonged to, so I called the sheriff's office, they sent a deputy. We, the deputy and I went to the home, explained what had happened. We were told the dog had never left his yard and no way he could have killed the chickens. We left, however I left them with one warning. That if by chance the dog got out of the yard and into my chickens, I would put him down.
That very night, I hear the commotion in the coop, sure enough it's the dog. I promptly lay him out with a 20 ga rifled slug. The noise of the gun going off was considerable, so the next sound I hear is the across the road nieghbor calling "here spot--here spot--here spot". Well I am going to tell you spot never responded. I called the sheriff, they responded by sending a deputy to my home, guess what it is the same deputy that was at my home earlier. He goes over to the nieghbors tells'em spot has gone to meet his maker. I swear you could hear the catawalling from where I was at.
The next morning I get a visit from the sheriff, seems as if my nieghbors have filed charges against me for "cruelty to an animal". It is illegal to kill an animal yourself. Just exactly what I was suppose to do I don't know, and to this day I am still not sure. I guess just keep buying chickens to supply the dog with sport. I was required to follow the deputy to his office, post a property bond and then I was ROR.
When I got in touch with a lawyer, he advised me to file charges against my nieghbors for the property damages. This I promptly did. The same deputy then makes a trip to the nieghbor's place. The amount of screaming, catawallin, comming from that house was terrible. I imagine that they did not cooperate like I had, the dog's owner was hauled off in hand cuffs.
I wish I could tell you the story had a happy ending, but this is not the case. Both sets of charges were heard at the same time in front of the same judge. The upshot was he paid for his and I paid for mine.
Sorry about the length. In th OP's case the dog's owner has already refused to take responsibility. He is not likely to start now. Some times peaceful people are backed into a corner that leaves them with no alternative than to take actions they would not normally have taken.