If two people of different ethnic backgrounds were guilty of the same crime, but only one of them were accused and tried, this would be a violation of

Due process and equal protection under the law-- due process requires laws be carried out fairly and equally. 

The laws of the US are suppose to be "blind" in particular for the justice system. Despite the sex, race, or origin of a person laws should be executed and judged equally. Despite the expectation the system does fall short because it relies on the unbiased thinking of the citizen which is difficult to come by. As a result the whole corrections system deals with the issues like the example in the question where race, ethnicity, sex, and social class can determine the outcome of arrests and ruling on laws.