A 501c3 is a tax exempt organization. Your tax exemption letter verifies that you are a non-profit. You should see a long number in that letter, which is the PTA's EIN (a federal ID number similar to a social security number).
If you have further concerns or want to know more about the PTA mission statement, board, or articles of incorporation, you can contact your state's attorney office or IRS office, and they will have copies of the papers originally filed by the PTA to qualify it as a non-profit.
