Believe it that a bill of sale, even from a police department, does NOT trump federal law, no matter what it says.
Some time back, a fellow got himself appointed police chief in a small town and promptly ordered a couple of dozen MGs and SMGs which he sold to his friends. BATFE wondered exactly how much crime there was in a town of less than 1500 people and investigated. The ex-chief may still be in jail; the guns were seized and presumably are now in the hands of legitimate LEO's.
Just one more note on the subject of police M14s. A while back, someone advertised an ex-police M14 for sale, supposedly converted to semi-auto by the Army and legal to sell. Just for fun, I called him and he assured me that he was the owner of a gun store, that the gun was legal and could be shipped to any FFL dealer. But that was the second call. On the first call, I forgot about the time zone difference, and called an hour too early. The voice mail kicked in to tell me that "AGENT Smith is not at his desk." AGENT?
A sucker would have bought the gun, then a few weeks or months later, the feds would have shown up with "information received" that there was an illegal machinegun on the premises. BATFE gets credit for arresting a "potential terrorist", the local cops bask in the reflected glory, the press gets a story involving machineguns, and everyone is happy. Oh, except for the sucker, who if he is lucky may get probation and a big fine instead of jail time.