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This is a meaningless question.
Assuming the question means race as in white people vs black people. Homo neanderthalis originated before any Homo sapiens existed. So if race means some kind of Homo sapiens, Neander is not of any human race any more than a chimpanzee is of the black or ace.
If you men skin color, no one really knows. Possibly, like humans and other widely distributed species of animals, Neander gloried in more than one skin color.
If you mean genetics, the ancestral human interbred with Neanderthal so that modern humans outside of Africans show some traces of Neanderthal ancestry.