I don't know the procedures, but to be President it's a requirement to be 35 years old and a native born American.
A birth certificate is about the only way to document both.
Supposedly McCain is not native born.
Presumably, if that was in doubt, there would be a lawsuit of some sort at which point evidence of all kinds, including birth certificates would be admissible.
I just looked it up.
McCain was born in Coco Solo, Panama Canal Zone, Panama.