It depends on what type of public building. But generally it will go to State.
an incumbent
He didn't serve in a public office but he was a Reverend which is like a holy person. He was just a famous person!
In most every state a FELONY conviction will bar a person from holding public office.
an Official
Canidate
candidate
May a person inherit the benefits of holding public office from an ancestor and what article of US Constitution?
In general, a politician.
civil servant
civil servant
Any trial court, federal or state, has the power to make a ruling like this. The rulings are always subject to appeal up through to the state or Federal Supreme Court. Even a state court ruling on the issue may be taken to the US Supreme Court.
No citizen should be banned from public office if they are otherwise qualified.