Doubt it'd even have one? While lots of firearms manufacturers used some sort of a serial number system, they weren't required until the late 60s. Remington serial #ed all their rifles, I have a M24 Gallery Gun that was built in the early '20s, and it's a got a serial #. The Model 12's # is probably on the tang or under the front of the receiver, like my M24.
Dad's old Stevens 86D, which I have now, isn't numbered anywhere except for some patent numbers which don't illuminate when it was made. I'm guessing it was made in the mid to late '30s.
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Not true poconojack, I have a Rem. Mdl 34 made 1932-35 and it is Ser. Boy, we have been all over the place on this topic.
I wonder where the truth lies and why Remington made it so difficult. Didn't state that some 22 rifles did not have serial #'s prior to 1968.rather, indicated that manufacturers were not required to serialize 22 rifles before the 1968 Gun Control Act. Can't recall the source but, read somewhere that manufacturers typically did not serialize the less expensive models of 22 rifles in their lines.