Tribal Nations are the only recognized arbiter of belonging to or being a member of a tribe. No other agency or arm of any government has that responsibility, other than the particular tribe to which a person claims to belong.
Every tribe has its own membership criteria; some go on blood quantum, others on descent, but whatever the criteria it is the tribe’s enrollment office that has final say on whether a person may be a member. Anyone can claim Indian heritage, but only the tribe can grant official membership.
Image above is of ‘Blood Quantum Earrings’ by Chickasaw jeweler Kristen Dorsey, from kristendorseydesigns.com.