The Constitution says an ineligible person cannot serve as President.
I would think that the state requirement for ballot placement is that the candidate and party by requesting placement are attesting to the candidate’s qualifications. If those qualifications are not met then the candidate misrepresented himself and, depending on state law, that candidacy could be judged null and void. Like I said an interesting exercise in federalism. Not that this is going to happen because I believe Godot will show up before any evidence that Obama is not a natural born citizen, but it makes for interesting speculation.