In Kentucky, to the best of my knowledge, FFL (Federal Firearms License?) dealers, meaning gun stores, must fill out a form recording the gun serial number upon purchase. This form stays with the private dealer, and does not get sent to the government as far as I know. However, if the ATF wants to come and inspect their records to investigate a crime, they can do so at anytime.
In my opinion, this creates a risk of national registration of existing firearms, at the whim of a Liberal congress. All they have to do is pass a law to confiscate the forms.
There is no requirement for this form for a private sale.