well, since it got closed on the other side.....
This is the closest I could find with a quick search....
The link is here...
CHAPTER 12. RECORDKEEPING
Section 12.1 Maintaining proof of registration. The NFA requires that a person possessing a firearm
registered in the National Firearms Registration and Transfer Record (NFRTR) retain proof of
registration which must be made available to the Attorney General, specifically an ATF agent or
investigator, upon request.184 Proof of registration would be on a Form 1 registering a firearm to its
maker, Form 2 registering a firearm to an importer or manufacturer, or a Form 3, 4, or 5 showing
registration of a firearm to a transferee.
Most of this all deals with federal law and the ATF. You may or may not be required by your states laws to provide the same info, but I dont know, you'll have to look at that end with your state.
The range is probably more concerned with their liability than anything else. From experience, many havent any idea as to what is or isnt legal, but it is their range, so you have to choose what you want to do. Many if not most ranges these days, wont even allow them on the range, which can be frustrating, especially when the reasons they give are total BS and incorrect. Insurance also has a lot to do with it. Oh well, such is life for a tax stamp holder in the world of know it alls.