Since the Ha Nhi originally came from Tibet, it is not surprising that their language is Sino-Tibetan.  This they share with the majority of Chinese, which mostly speak Sino-Tibetan languages.  But Ha Nhi is part of the Tibeto-Burman offshoot, and so the relationship with Chinese is somewhat distant.

The language falls within the Yi (LoLo) branch of the Tibeto-Burman family.  A major dialect of the Ha Nhi is called "Jeu G'oe" widely spoken by most in Thailand, southwestern Yunnan, China, and Northeastern Laos.  It is not clear if this is the major dialect in Vietnam.

This means that the Ha Nhi language is linguistically unrelated to Vietnamese, the national language of the country.