Can we require medical tests or treatment?

Q. I’m confused about when we can require physical exams or treatment. We now make employees undergo a fitness-for-duty exam when we think there is a physical or psychological reason that impairs the employee’s ability to perform the job. We also use last-chance agreements requiring medical treatment for an employee to earn reinstatement after a discharge, such as for alcohol or drug abuse. Are we courting trouble? —D.J., Michigan