In New York state, you need a note (at least in Livingston county) that tells them your covering is for religious purposes. I am ordained clergy through the Church of the Ancient Paths .
I offer my services in assisting you if you are local to me and in need of a note stating that your covering is for religious purposes. The letter will be sent to you via registered mail, this way everyone has a record that it has been sent and received. I will also be willing to assist in getting the letter notarized. I do not know if there will be fees associated with this process. (I need to look that up.)
Prior to sending you this letter, you and I will have an 'official' discussion where we talk about your covering needs - read you tell me why you cover and any other situations you may need an official letter explaining that you cover for religious purposes, as well as anything else you deep pertinent to the discussion.
If you are not local to me, I will do my best to assist you in your effort to have your right to headcovering as religious expression assured. There will be more information forthcoming on this matter over the next several months.