In many areas shooting a dog with a bb gun or shooting with any other gun with the intention of wounding is considered animal cruelty. Shooting them dead to protect your animals is not and is legal in most areas
It is suppose to be legal around here to kill a dog on your property if it even attacks a farm animal, or even a dog or cat on your land. However around here the police say no. Even though it is a county law, they say no.