Do all part time employees have to be paid on an hourly basis?

by Phil
(Michigan)

Do all part time employees have to be paid on an hourly basis? For example, our Janitor works less than 20 hours per week. can we pay him a set salary to perform his tasks? Or does he need to keep a timecard and then we need to jump through the extra hoops to calculate his payroll taxes / withholding each pay period as his time worked may differ from week to week?