Sorry but there is such certification, each state must certify the candidate as eligible to run. There is nothing in place to require proving it however. Still, he was illegally certified because each state failed to check out whether or not he was a natural born citizen.
Do you have a reference for this? It certainly isn't in the constitution, but might be in state or federal law.
From what I know about it, some states have requirements to certify eligibility for state office but they have no such authority for federal office.
As I understand it, one of the minor party presidential candidates who was on the ballot in many states was openly a naturalized citizen, thus not eligible under any interpretation.