No. Like most of the US, there is no requirement to register ordinary rifles, shotguns, or handguns in KY.
Basically, no. There are several parts to the answer: if you are in the U.S. most states don't require registration, and there is no federal registration. If you do live in one of the few states that...
You find a book with serial number information and look it up. You find a book with serial number information and look it up.
You can't
Google it. You should be able to find something from your local police department. If not, go to your police station.
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