Real Estate Law
Have Real Estate Law Questions? Ask a Real Estate Lawyer.
First, you have the right to defend yourself, your family, and others who are located on your property from any animal that may come on your land and threaten them. You should avoid killing this animal if at all possible to avoid potential liability, however you have the right to defend yourself and your family.
Second, your county has an ordinance against dogs such as this and proscribes penalties that can be enforced by your county animal control agency. I recommend taking two steps... 1) photograph or record the animal every time he comes on your property... 2) report the matter to the authorities and insist they enforce the following ordinance.
Finally, your neighbor could be sued for the actions of his dog after he has been put on notice of the dog's behavior. For this reason I recommend you have a local attorney send him a certified letter advising him of his dog's dangerous behavior and that he will be held liable for any resulting damages (civil and criminal).
Please reply if I can help further.
It is possible to be sued for shooting a trespassing dog who is not an immediate threat to your safety or the safety of others on your property. You may also be prosecuted for shooting the dog though I would doubt any such action would be considered given your description of the history. I would simply prefer you take the above actions to prevent any potential hassles.