You don’t necessarily need to change their classification, but the minimum salary for exempt employees—which will be determined by federal or state law—can’t be prorated based on the number of hours worked. This means you can only keep the employee as exempt if, after the salary reduction, they still make at least the applicable minimum salary. If their new pay is below the minimum for exemption, you’ll need to reclassify them as nonexempt and pay them based on the number of hours they work.
This Q&A does not constitute legal advice and does not address state or local law.