Unlikely, car insurance a better choice. Responding to your question though, I would have to say that home owner's insurance in Kentucky could cover it. It is more likely than not however, that car insurance would be the one to cover a hit and run to your car. This greatly depends on your insurance however. There is something on the Declarations page of your Auto insurance policy called Underinsured/Uninsured Motorist bodily injury and property damage listed. This is probably where you would find coverage.
However, someone who has been involved in a hit and run can be in a lot of legal trouble. First of all, an accident is an accident, whether or not it happened with a human in the car. Fleeing the scene of an accident is against the law and is classified as a felony.