How can I verify an individuals U.S. citizenship?

Ask for a birth certificate.

Passport, or certified birth certificate (with raised seal), or naturalization certificate, or certificate of citizenship, or consular report of birth abroad.

Who is the person? Unless you have a valid legal reason for asking them to produce one of the documents above you can't really.

Or do you merely need to verify their legal status to work in the US.

E-Verify