The short answer is yes and no. North Carolina exempts public schools (and most other governmental entities) in the same way it does non-profits. They are exempt, but they must pay sales tax at the point of sale, then file to be reimbursed by the state.
This round-about process may seem a bit backwards. But walk a mile in a retailer's shoes; they are already required to collect, track, and remit sales tax for the state (without getting paid for the work). What would it be like if you had to also verify each person/entity’s non-profit status, not collect their sales tax, and track and report those sales separately? A freaking nightmare. Therefore, in an act of benevolence, the DOR has established a compromise: that public schools non-profits pay sales tax at the retail point of sale (like everyone else), but then (unlike everyone else) they can request that the amounts be paid back to them by the state.
(For confirmation of the rule, please see Sales Tax Technical Bulletin 18, items 1 and 4.)
If you work for a public school and would like to know how to file for reimbursement for sales tax, it would be best to contact your school's finance office for next steps. There will probably be an exemption number already set up for your school or district. Keep in mind that if you yourself are being reimbursed by your school for supplies or other expenses, the sales tax paid on your expenses is not eligible for reimbursement. It's only eligible on purchases made by the school directly. Another good reason to check with your finance office.
Hope this has helped! Best wishes.