Public Officers and Employees; Requiring that, beginning on a specified date, secretaries and executive directors of departments, chief administrative officers of certain units of state government, members of commissions and licensing boards, chairs of governing boards or certain chief executives of certain statewide entities, or any persons appointed to hold state office in the executive branch of state government be United States citizens and residents of this state; providing that a specified provision applies to each such offices; requiring that, beginning on a specified date, members of the board of trustees for state universities be United States citizens and residents of this state or graduates of the state university that the board oversees.