[Raider Sam]

So the 10th Amendment addresses who is responsible for determining the President’s eligibility? Who does it say does it?

If you are saying this should be an issue left to the states to determine, then I agree. But it doesnt say that Congress can do it. The 20th says how Congress will replace a President, but only after he has been shown ineligible.

[edge919]

So the 10th Amendment addresses who is responsible for determining the President’s eligibility? Who does it say does it?

"The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people." Since there's nothing in the Constitution that delegates the power to determine the president's eligibility, this would fall to the states or to the people. This is consistent with how states require candidates to sign affadavits or ballot nomination forms. The states hold elections and the states are responsible for choosing electors.