Are you working for the city/county/state government or a private company? I worked for the government, so I never had to have a medical exam at all.
If you're working for a private company, I honestly can't remember what the rules for medical stuff was since it didn't apply to what I was doing. This site
here does state that in order to get a permit, you must "Certify whether you comply with federal medical requirements for a CDL (and provide the medical examiner's licensing number)", but keep in mind that's not an official site, so take it with a grain of salt.