We apply computational dialog methods to police body-worn camera footage to model conversations between police officers and community members in traffic stops. Relying on the theory of institutional talk, we develop a labeling scheme for police speech during traffic stops, and a tagger to detect institutional dialog acts (Reasons, Searches, Offering Help) from transcribed text at the turn (78% F-score) and stop (89% F-score) level. We then develop speech recognition and segmentation algorithms to detect these acts at the stop level from raw camera audio (81% F-score, with even higher accuracy for crucial acts like conveying the reason for the stop). We demonstrate that the dialog structures produced by our tagger could reveal whether officers follow law enforcement norms like introducing themselves, explaining the reason for the stop, and asking permission for searches. This work may therefore inform and aid efforts to ensure the procedural justice of police-community interactions.