Police checking for illegal drugs are much more likely to search the vehicles of African-American motorists than those of white motorists. This paper develops a model of police and motorist behavior that suggests an empirical test for distinguishing whether this disparity is due to racial prejudice or to the police's objective to maximize arrests. When applied to vehicle search data from Maryland, our test results are consistent with the hypothesis of no racial prejudice against African-American motorists. However, if police have utility only for searches yielding large drug finds, then our analysis would suggest bias against white drivers. The model's prediction regarding nonrace characteristics is also largely supported by the data.