Answers to tricky HR questions: What's the rule on mandatory physicals for new hires?

Our team of experts fields real-life, everyday questions from HR managers and gives practical answers that can be applied by any HR pro in the same situation. Today’s question: What are the limitations on having new hires take physical exams as a requirement for employment?
We’re considering mandatory new-hire physicals, but we want to make sure we’re following all the rules and regulations.
What should we watch out for? And is it legal to request a physical before actually hiring the person?
Upon making an offer of employment – but not before – you can require a physical exam so long as you meet two criteria, according to employment lawyer Jane Dalton:
1. The physicals are given to all new hires who fill similarly situated positions, and
2. The results are kept confidential and used only to determine whether the person can perform the essential functions of the job.