A school might want an immunization record to make sure you've had specific immunizations, but I've never heard of one asking for full medical records. Many schools do require criminal background checks though, so if you had any drug-related legal issues there may be an issue.
Drug and legal issues can affect you at several levels, not just getting into PT school. Many clinical sites require criminal background checks, and they may not allow you to be at their site. It may also affect your ability to be licensed.