I'm going to Ross, so my requirements will probably be a bit different than schools in the States. I had to get tested for HIV, TB, and syphilis (VDRL), but these are required by the St Kitts government in order to get my student visa, not by the school itself. The school requires vaccines for Tetanus, Hepatitis A and B, and Rabies, plus a regular physical exam.
On the non-medical side, I also have to get a criminal background check, but again, that's for the student visa, not the school. Hope this helps you! 🙂