I am licensed in the Commonwealth of Virginia, answering your query and my answer do not create an attorney-client relationship and I am not providing you legal advice. You should speak with an attorney to whom you have provided all the facts, before you take steps that may impact your legal rights--or rights to recovery of damages. I wish you the best of luck with your situation.
Pursuant to KRS § 263.160 (2011), Operations exempt from law, a dead animal must be delivered to a proper facility for disposal. So, although it doesn't say precisely, I think the answer is no, you cannot. On the other hand, it happens so unless you bury the animal too close to a water source, it somehow fouls your neighbors property, or you don't bury it deep enough and it is dug up by other animals, you are probably okay.
If you want a definitive answer, contact the Kentucky Bar Association: www.kybar.org/
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.