In this day and age, many districts have their policies on their website. In the old days, students got a handbook at the beginning of the year that addressed policies on any number of matters, to include dress codes.
You need to know what YOUR district covers...no place else is relevant to the discussion. Also relevant will be how strongly your parents will go to bat for you against the district...
As to what transgender people carry, I have no idea. Even with a letter, there is no guarantee that it will be recognized by any entity. As a transsexual, I never carried anything in the way of a letter...although that was also back in a pre-9/11 world. Hell, it was a pre-Clinton world...