[anonymouskimmer]

Things have progressed since the 1930s. At this point Superman would be a stateless person, and there are presumably a variety of international treaties that govern how he can be treated.

I also believe that his alter ego, Clark Kent, is documented as an adopted child of the Kents. It would have been much easier back in the day for infants to be recognized as natural born US citizens regardless of whether or not they were as home births were much more frequent, and IDs such as social security numbers weren't automatically given to infants at birth. Given Superman's discovery as a white appearing infant in Kansas, there would be no reason for the government to presume he was not a natural born citizen. And if they did presume this, they'd have to climb a mountain to legally prove it (not being accused of a crime, good luck getting a court to require a DNA test to show that he is a literal alien).

As for Superman the alter ego? How would anyone prove he isn't a US citizen? They don't even know who he is.

[29athrowaway]

Legally, Superman is undistinguishable from an object until granted personhood, or declared something else, like property or an animal.

[anonymouskimmer]

He was granted personhood with his adoption papers.

[29athrowaway]

If I adopt a cat from a shelter that doesn't make it a person.

[anonymouskimmer]

You don't get human adoption papers when buying cats from shelters. It's not even an adoption, per se, when it's a cat, we just call it that. Sam I am.