Art. 448  from Oldham and White (1859), 120, also gives a standard for racial definition.
Witnesses, who are incompetent.
Art. 448.  All Negroes and Indians, and all persons of mixed blood, descended from negro ancestry, to the third generation inclusive, though one ancestor of each generation may have been a white person, shall be incapable of being a witness in any case whatever, except for or against each other.[b]
George W. White and Williamson S. Oldham, eds. A Digest of the General Statute Laws of the State of Texas
(Austin, Tex.: Printed by J. Marshall & Co., 1859), 120 (link)
California – People v. Hall (1854) — Chinese testimony grouped with Black and Indian by construction, “Black” as generic term =df non-White, the reverse of arguments made in Texas 1845 state convention. / WBL 51ff
Unsurprisingly, this early social treatment of Chinese as akin to Blacks also found legal expression. For example, in the 1854 case People v. Hall the California Supreme Court heard the appeal of a White defendant challenging his conviction for murder. He appealed on the grounds that he was convicted only through the testimony of a Chinese witness, and that this testimony should have been excluded under an 1850 statute providing that “no Black, or Mulatto person, or Indian shall be allowed to give evidence in favor of, or against a White man.” The court agreed with the defendant that the Chinese witness was barred from testifying by the 1850 statute, reasoning that Indians originally migrated from Asia, and so all Asians were conversely also Indian, and that, at any rate, “Black” was a  generic term encompassing all non-Whites, and thus included Chinese persons. This legal equation of Chinese and Black status was not temporally or geographically unique. Three-quarters of a century later and across the country, Mississippi’s Supreme Court reached a similar decision, holding in 1925 that school segregation laws targeting the “colored race” barred children of Chinese descent from attending schools for White children. Given their social and legal negroization, it may well have been easier for the Chinese and other immigrants to argue their qualification for citizenship as Blacks rather than as Whites.
Ian F. Haney López, White By Law: The Legal Construction of Race
(New York: New York University Press, 1996), 51ff.