The word "China", referring to a particular tribe, is found in Manu Smriti 10.44:
10.43. But in consequence of the omission of the sacred rites, and of their not consulting Brahmanas, the following tribes of Kshatriyas
have gradually sunk in this world to the condition of Sudras
10.44. (Viz.) the Paundrakas, the Chodas, the Dravidas, the Kambogas, the Yavanas, the Sakas, the Paradas, the Pahlavas, the Chinas, the
Kiratas, and the Daradas.
10.45. All those tribes in this world, which are excluded from (the community of) those born from the mouth, the arms, the thighs, and the
feet (of Brahman), are called Dasyus, whether they speak the language
of the Mlecchas (barbarians) or that of the Aryans
The relevant verse in Sanskrit is:
PoundrakAsha chauda drAvidAh kambojA yavanAh shakAh |
pahlavAsh chinAh kirAtA daradA khashA ||
So, according to Manu Smriti, all those tribes, including the China tribe, were originally Kshatriyas, but due to non-performance purificatory and sacred rites, they became VrAtyas and degraded themselves to the status of the Sudras.