Shotguns and .22 rimfire rifles made prior to 1968 are sometimes found without serial numbers. It was legal for them to be made without serial numbers, prior to the 1968 Gun Control Act.
However, I don't believe it's been legal to make a pistol or rifle without serial numbers for a very long time in this country. It may even predate the 1934 Firearms Act. I'd have to read the blamed thing to find out, and I'm too old and grumpy to do that ...
But yes, if it EVER possessed a serial number and that serial number was ground off --- it's already been involved in a crime.
If it was taken from the federal government, there's yet another crime.
I certainly wouldn't want to get caught with it, especially as a concealed weapon or on federal land (Bureau of Land Management, Forest Service, etc.), because you've just compounded your problems.
I would get rid of it. Not worth the tremendous legal hassle and bills you'd incur by being caught with it. Or call the local ATF office from a pay phone on the other side of town (to confound tracing), tell the agent the problem, and ask if you can have it restamped with an approved serial number.
If you can't, ask how you can turn it over to the ATF for disposal without being painted as a terrorist.
Use a code name. Tell them your name is "Marshall."