You will have to look at your local laws, however I would be very surpirsed to hear that Ky or Tn charge you a property tax on the item. Sales tax...you can count on that as a one time deal.
Your situation is a little more complicated as you are purchasing the boat in Ohio, you live in Tn, and you say the boat will be kept in Ky. It is possible that you can keep the boat in Ky and pay Ky taxes and documentation on it. You don't say how big this boat is, if it will be stored in KY or TN, etc.. I would contact your local, in this case both KY and TN, Secretary of States and see how they feel you should proceed. You don't want to get caught in a pissing contest between the two of them on which state you owe the tax to. You also don't want to play any games to save any difference in tax amounts unless you are certain that you are legal ly covered. Tax hassles are never worth it.