The federal government does not require work permits or proof-of-age certificates for a minor to be employed. Many states, however, do require them for workers of certain ages. In addition to state labor departments, school guidance counselors might know if permits or proof-of-age certificates are required in that particular state.
The Department of Labor will issue age certificates if the minor employee's state does not issue them, or if the minor is requested by his or her employer to provide one. However, the vast majority of age certificates are issued by states.
https://www.dol.gov/general/topic/youthlabor/workpermitsagecert