This paper considers the use of outcomes-based tests for detecting racial bias in the context of police searches of motor vehicles. It shows that the test proposed in Knowles, Persico and Todd (2001) can also be applied in a more general environment where police officers are heterogenous in their tastes for discrimination and in their costs of search and motorists are heterogeneous in their benefits and costs from criminal behavior. We characterize the police and motorist decision problems in a game theoretic framework and establish properties of the equilibrium. We also extend of the model to the case where drivers' characteristics are mutable in the sense that drivers can adapt some of their characteristics to reduce the probability of being monitored. After developing the theory that justifies the application of outcomes- based tests, we apply the tests to data on police searches of motor vehicles gathered by the Wichita Police department. The empirical findings are consistent with the notion that police in Wichita choose their search strategies to maximize successful searches, and not out of racial bias.