The statute reads: "Every motorboat on the waters of this state shall be numbered and currently registered in accordance with the provisions of this chapter." To me, that means public and private waters. Go to http://fw.ky.gov/Navigation.asp?cid=102 and click on "Boating Regulations" or "Boating Statutes" and you can check out the regs yourself. What I haven't been able to find is a good definition of "motorboat." That may sound silly, but my understanding has always been that those regulations only apply to boats with internal combustion motors. But I can't find any documentation to back that up, so I would call DMV just to be sure. That's where you get the license, so they should know.