I live near a path where hundreds of people walk their dogs every day. my dogs were out playing in the yard today and someone was walking their pitbull and it came up to my fence and got in a little scuffle with my dog. The pitbull got a bite and my dogs nose is bitten as well. My dogs never got out of the yard...am i liable for that other dog being bit even though mine was bit too and in ITS OWN YARD!! plus i have a cattle dog and the dog that bit my dog was a pittbull...come on!!
Since both dogs were bitten, it's probably a wash but at some point someone is going to sue you - whether the suit is successful is another matter. You need to do something to keep outside dogs from being able to put their noses through your fence.