Among black respondents, 24% said Gov. Ralph Northam should resign, while 38% were against it, 22% refused to answer and the rest weren’t sure. As for Mr. Fairfax, 8% of black residents surveyed think he should step down, 29% didn’t think he should, 41% weren’t sure and 22% wouldn’t answer.

Residents are “just not sure what to think because this is unprecedented,” said Larry Sabato, who directs the University of Virginia’s Center for Politics. “They are clearly waiting and seeing.”

Among all survey respondents, 31% said Mr. Northam should resign, while 43% said he shouldn’t, and 26% were either unsure or didn’t answer, according to results reviewed by The Wall Street Journal. For Mr. Fairfax, 35% said they believe he should resign while 25% said he shouldn’t, and 40% were undecided or refused to answer.