I had a neighbor who hated me, hated my dogs. No reason, just because I asked her to please stop letting her dogs jump on my fence and bark at my dogs.I talked to the Animal Control officer in the town next door. She said they reserve "dog at large" tickets for the dog raiding the neighbor's trash while the owner is asleep on the couch type incidents. Anything else, usually a different law applies (or nothing applies, and there is no ticket). For example, dog raiding a chicken coop would not be at large, but either a menace or vicious- different ticket.
This whole thing seems like such a waste of time and effort- but I am of course taking it very seriously now. With dogs' safety #1 priority.
When Shadow was about 4 months old she slipped out my screen door on day and bolted out to see the dogs walking by. Husband was hot on her heels and scooped her up immediately but not before he got bitten by crazy ladies dog and screamed at for Shadow attacking them.
AC showed up and I was ultimately given a ticket for dog at large, which I deserved, but the story she gave was that Sabi had leaped over the fence and attacked them and they only escaped injury because her dog managed to fight Sabi off and drive her back into my yard. Fortunately the guy had half a brain and realized that Sabi was not involved and little wiggle butt Shadow had not "attacked" anything. He was a good guy, but over the course of the next few years I had AC and/or the police at my door at least once a week. And I always had to go back and explain that yes I had been given a ticket, but the complaint on file was totally false.
Much more frightening was that about a week after the incident I went out with the girls to check the front yard in the morning and noted an oddly colored patch of snow in the center of the yard. Testing revealed that the substance was antifreeze and the placement of it meant someone had walked into my yard to put it there. I don't ever keep antifreeze on the property. Two months later a package of strychnine soaked ham appeared next to my doorstep. Again someone had to enter my yard to place it there.
Get a lawyer and be very, very careful. With you and your dogs.