One thing I've learned about the US justice system from watching a lot of criminology dramas (not that this is valid source of inferences, but it causes me to look things up for real):

You can choose to prosecute a case with basically any evidence (including "no evidence.") In a jury trial, it's up to the jury to decide whether the suspect is guilty—i.e. jury nullification goes both ways, and a jury can return a "guilty" vote despite a complete absence of a case, just because they feel like it. (A judge does have the ability to overrule any guilty verdict they feel was reached unjustly, but in the sorts of situations you'd expect a community biased enough to return a guilty verdict in absence of evidence, you'd also expect the judge—if they're a member of the same community—to be biased as well.)

Usually, though, because juries are almost never that biased (and are not aware of jury nullification), prosecutors just "decline to prosecute" cases that they don't think have enough evidence to sway a jury.