Is there justice in Maycomb County?

One would have to say no. Tom Robinson has been falsely convicted of the rape and assault of Mayella Ewell. This wasn't even a borderline case; it was physically impossible for Tom to have carried out the deed. But in Maycomb County, as elsewhere in the Deep South, that doesn't really matter, because the trial of a black man accused of rape has less to do with achieving justice and more to do with reinforcing the dominance of the white race.
As soon as Tom was accused of the crime, the vast majority of people in Maycomb made up their minds that he was guilty as sin. Why? Because Tom is black, and in the South at that time, the prevailing prejudice held that black men were always on the lookout for white women to rape and as such needed to be kept firmly in line by the law.
Mayella's accusation, though patently false, is tantamount to a conviction in such a deeply racist society. The members of the jury—all but one of them, anyway—have already made up their minds as to Tom's guilt before even setting foot inside the courtroom. They know what's expected of them; they know that their deliberations have absolutely nothing to do with any meaningful notion of justice, but everything to do with keeping African Americans firmly in their place.

Judging from the verdict of the Tom Robinson trial, one could argue that there is no justice in Maycomb County. Tom Robinson becomes the victim of racial injustice after being wrongly convicted of assaulting and raping Mayella Ewell. During the trial, Atticus proves that Bob and Mayella's stories were fabricated and shows that Bob had the motivation to assault his daughter. Atticus also proves that Tom Robinson could not have inflicted the injuries to Mayella's face and neck because of his obvious physical handicap. Despite Atticus's efforts, the racist jury wrongly convicts Tom Robinson of assaulting and raping Mayella simply because he is black. This blatant example of racial injustice is enough evidence to state that there is no justice in Maycomb County. In addition to Tom becoming a victim of racial injustice, the Old Sarum bunch is not punished for attempting to lynch Tom before the trial, and Bob Ewell is allowed to freely roam throughout the community after committing obvious perjury.