African American motorists in the United States are more likely than white motorists to have their cars searched by police checking for illegal drugs and other contraband. The courts are faced with the task of deciding on the basis of traffic-stop data whether police are basing their decisions to stop cars on the race of the driver. We develop a model of law enforcement for a popula- tion with two racial types who also differ along other dimensions relevant to criminal behavior. We discuss why a simple test commonly applied by the courts is inadequate when the econometrician observes only a subset of the characteristics observed by the policemen. Next, we show how to construct a test for whether differential treatment is motivated purely out of efficiency grounds, i.e. to maximize the number of arrests, or rejects racial prejudice. The test is valid even when the set of characteristics observed by the police- men are only partially observable by the econometrician. We apply the tests for discrimination to traffic stop data from Maryland. Finally, we present a simple analysis of the tradeoff between efficiency and fairness.