EEOC: “NATIVE AMERICAN OR ALASKAN NATIVE: Any person having origins in any of the original peoples of North America, and who maintains cultural identification through tribal affiliation or community recognition.”
Bureau of Indian Affairs: “The BIA generally defines an ‘Indian,’ who is eligible for BIA services, as an individual who is a ‘member’ of an Indian tribe, band, or community that is ‘recognized’ by the federal government; who lives on ‘or near’ a reservation; and who is of 1/4 or more Indian ancestry.”
Department of Justice: “As a general principle, an Indian is a person who is of some degree Indian blood and is recognized as an Indian by a Tribe and/or the United States. No single federal or tribal criterion establishes a person's identity as an Indian. Government agencies use differing criteria to determine eligibility for programs and services. Tribes also have varying eligibility criteria for membership.
“It is important to distinguish between the ethnological term ‘Indian’ and the political/legal term ‘Indian.’ The protections and services provided by the United States for tribal members flow not from an individual's status as an American Indian in an ethnological sense, but because the person is a member of a Tribe recognized by the United States and with which the United States has a special trust relationship.
(Well, I guess feds can say what an Indian is, since there are several definitions.)