can I sue his homeowner insurance or do I have to go after him in civil court.
You never sue someone's insurance - you sue THEM, and the insurance, if applicable, will cover the judgment up to their policy limit. The insurance will generally step in and provide legal representation but, the insured, and not the carrier, is the defendant. If all you want it vet bills, you can even use small claims court up for up to a few $K. If you to be made whole for the kind of pain and suffering that only large amounts of $$ can alleviate, you'll need a contingency fee lawyer who is willing to take the case to trial rather than settle (expect an uphill battle here, as dogs are generally considered property with a $$ value by the legal system).
Be conscious as to the import of MGL when acting in defense against a dog. You should be on solid legal ground if the dog is worrying (as in baring of teeth, not "causing of concern something bad will happen") you or your livestock. It is doubtful that a family pet will be considered "livestock", but if YOU are directly threatened by the dog, and properly explain this (legal counsel might not be a bad idea). You need to either arrange for assistance to the animal you shot, or dispatch the beast, to avoid charges of cruelty to animals. If they really want to "get you", there's always the firing with 150 ft or a roadway and 500 ft of an occupied dwelling charge. The legal outcome will depend as much on the political climate of your town and the political influence of the attacking dog's owner as the merits of the case so, as with any use of a gun, you need to be sure it is absolutely necessary.
Also, remember that all the dog owner has to say is "He threatened me with the gun after shooting my dog", and you'll be surrendering all your guns to the police, perhaps paying Dowd's ransom to transfer them to a friend with an LTC, and having a talk with an attorney about how many thousands (or tens of thousands) it will cost to defend the case instead of take a plea bargain that will leave you a prohibited person.
I recently stayed at a friend's house that was full of dogs (Goldens, a Beagle, a Pit and a Pommerian someone brings into his office). The beagle went after the pit bull to take some food away from it .... and the pit bull backed down. Perhaps knowing he could kill the beagle without working up a sweat was enough for him
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The selectmen can order a dog destroyed or removed from town. You need to decide if this is an avenue you will pursue.