In the UPS info...
"Any item that meets the definition of a firearm (including firearm mufflers or silencers) or a “frame” or “receiver” under federal law (including any partially complete, disassembled, or nonfunctional frame or receiver as defined by 27 CFR § 478.12) must be identified and bear a serial number in satisfaction of the requirements for identifying such items under federal law, including 27 CFR § 478.92 and/or 27 CFR § 479.102, regardless of whether any such items are otherwise exempt from or not subject to identification requirements under applicable law. This prohibition applies even before the effective date of 27 CFR § 478.12."
I think this says that all firearms must have a serial number regardless of whether it is required by law. A lot of older .22 are not serial numbered.
