The employee may remain a participating employee in the retirement system established under chapter 201, laws of 1937. To remain under the retirement system established under chapter 201, laws of 1937, the employee must exercise this option in writing, on a form provided by the department, at the time the employee is appointed to a state employee position. The employee shall exercise this option, in writing, no later than 10 days after the employee is appointed to a state employee position. An employee’s decision to remain a participating employee in the retirement system established under chapter 201, laws of 1937, is irrevocable during the period that the employee is holding a state employee position in the unit.