Here are the literal requirements for running for city council in Orem, Utah:
1. A candidate must be a United States citizen.
[Note: United States is not defined in the statute, therefore, common usage is the standing definition of the term]
2. A candidate must be at least 18 years old and a registered voter of the municipality.
3. A candidate must have resided in the city of Orem or recently annexed area for 12
consecutive months immediately preceding the election.
4. Any mentally incompetent person, any person convicted of a felony, or any person convicted of treason or a crime against the elective franchise may not hold office in this state until the right to vote or hold elective office is restored as provided by statute.
http://orem.org/index.php/elections/elections-a-voting-info
They even provide sample paperwork for people at this link:
http://orem.org/PDF/RO/CandidateGuide2013.pdf