Researchers often lack the necessary data to credibly estimate racial bias in policing. In particular, police administrative records lack information on civilians that police observe but do not investigate. In this paper, we show that if police racially discriminate when choosing whom to investigate, using administrative records to estimate racial bias in police behavior amounts to post-treatment conditioning, and renders many quantities of interest unidentified---even among investigated individuals---absent strong and untestable assumptions. In most cases, no set of controls can eliminate this statistical bias, the exact form of which we derive through principal stratification in a causal mediation framework. We develop a bias-correction procedure and nonparametric sharp bounds for race effects, replicate published findings, and show traditional estimation techniques can severely underestimate levels of racially biased policing or even mask discrimination entirely. We conclude by outlining a general and feasible design for future studies that is robust to this inferential snare.