If the use of lethal force is justified by a person with a service dog based on self defense, then the question in the OP is irrelevant. You are defending yourself and not the dog. The question in the OP is only relevant if the service dog is killed and the service dog owner does not have a reasonable fear of imminent death or serious bodily harm. According to the law, an animal is not a person. It is property. I don't think Kentucky has a statue for using deadly force to protect property. The actual circumstances will decide if you will be charged with murder, manslaughter or nothing.
As with all these of "could I shoot someone" discussion threads, the OP is asking the wrong question. You never ask "could I shoot someone"! The question is, "do I have to shoot someone". I highly recommend to either take a legal training class or get some legal reading material about what happens after the fight. Realize that you will get taken into custody and you will go through the legal system. You better immediately spend some money on a lawyer (several thousand Dollars) to protect yourself. You may be spending a night (or more) in jail. You will need to post bond and spend more money on the lawyer if you get charged.
In short, shooting someone is a life changer. It will impact your personal life forever. You may lose a lot of money, your job, friends, family members, your mental health, and possibly your freedom. There is a basic cost/benefit trade off. Are the benefits of shooting someone outweigh these costs. If you defend your own life or the life of a loved one, it obviously is. Would you be able to live without your service dog, or would you rather spend some time in prison, knowing that your service dog is alive?
Resources:
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5 Things Every Reasonable Gun Owner Ought To Know