I wouldn’t have thought so, but Justin Wolfers, writing with Joseph Price, says maybe yes:
…during the 13 seasons from 1991 through 2004, white referees called fouls at a greater rate against black players than against white players…[the authors] found a corresponding bias in which black officials called fouls more frequently against white players, though that tendency was not as strong.
Here is the paper. The effect is big enough that an all-white team would, all other things equal, win two extra games over the course of an 82-game season. A panel of three independent experts has judged that the Wolfers-Price analysis is more convincing than a David Stern-sanctioned rebuttal that no bias is present.
The NYT web site is slow this morning, try back later if the first link is giving you trouble.