Social media has emerged as a promising resource for police to connect with citizens for collective action. However the attributes of police citizen interactions on social media remain under-explored. In this paper, we utilise official and public Facebook pages of several police departments in India to study the patterns of engagement, emotions, and social processes between citizens and police in the context of day-to-day policing. We examine two prominent discussion threads: police initiated and citizen initiated. We find that topics exchanged in police initiated discussions are more focussed than citizen initiated threads; police focused on topics concerning safety awareness programs, action reports, and information regarding policing activities. Compared to police initiated discussions, citizen initiated discussions show lower engagement. Further, discussions involving both police and citizens show higher negative emotions, anger and arousal than citizen only discussions; these interventions involving both reveal a stronger notion of a collective identity. We discuss the implications of our work in designing technological support for improved policing and to help understand citizen opinions, safety concerns and well-being via social media.