Someone recently posted about a transfer at MSP and in doing the paperwork something came up regarding model/serial no.IIRC the trooper hit a few keys and BAM there it was.
I did a regulated (2 items) sale through the Rockville MSP barracks last year.
After the guns were examined and the paperwork completed, the officer had us wait a few minutes while another officer handled the paperwork while working on the computer and using the phone.
He then came to the window to explain about the 7 day wait, and then the legal exchange etc. He added "I just confirmed you are the lawful owner and that you both are Designated Collectors, so there shouldn't be a problem" I asked if they kept this on file for all of my gun purchases and he just laughed. Nice guy, smooth transaction but also a confirmation of my suspicions.
I am positive they keep a record of regulated purchases in this state, how accurate it is I don't know.