The liability belongs to the home out of which the problem arose. Take pictures of the dog and its bite. (so they can't switch in some other mess on you) Make notes of the time, place, and their complaint. Register every witness. And take it to your home owner's liability insurance agent.
Just be glad it did not bite a child.
We had a kid go into our garage, get our hatchet, and cut off the tip of his finger. Then later, the same one, playing in a tree in our front yard fell and broke his arm. Our home owner's liability insurance covered both incidents.