US Constitution, Article II, Section 1, Clause 2.
That's the clause that spells out the rules around presidential electors, and places most of the authority for this with the states.
AFAICT, this gives each state the authority to oversee how electors are chosen and instructed, which would necessarily have to include the authority around issues like eligibility requirements to be on the state ballot.
That being said, faithless electors are a thing, so if an ineligible presidential candidate got EC votes, it would be up to the joint session of Congress to raise the objection and reject those invalid votes through their process.