Dog attacking

Long story short my dog got out and went to the neighbors. My husband went straight over there to get him and our dog and their dog was fighting. My husband put a leash on our dog and then their dog attacked ours. Neighbors called the cops and animal control came today. They gave us a warning and said if they see our dog out they will pick him up. Now my neighbor wants to sue us for property damages and Bill's. My question is can she do this? I've tried looking it up but everything I see is about a dog attacking a human not a dog on dog situation. We are in Tennessee. I just kinda figure if animal control gave us a warning if they thought it was bad enough that they wouldve done something today when they came.