When I looked at the constitution and fed law, I found that there is a requirement for age and for being “natural born”, but no process to check that, nobody who officially says, yup, she’s OK to run, she’s natural born.
You file to run in 50 states, not federally, and the states I looked at have no check mark on the forms for “natural born”.
The issue came up with Goldwater and earlier with McCain (Arizona Territory and Canal Zone) but there is no federal vetting process I could find.
Or, the birth certificate states that his father is actually (the man who Obama more closely resembles) Frank Marshall Davis.
I tried to find something also and couldn’t.