This article considers the use of outcomes-based tests for detecting racial bias in the context of police searches of motor vehicles. We characterise the police and motorist decision problems in a game theoretic framework, where police encounter motorists and decide whether to search them and motorists decide whether to carry contraband. Our modelling framework generalises that of Knowles et al. (2001). 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 maximise successful searches.