Police agencies across the globe are increasingly using Online Social Media (OSM) to acquire intelligence and connect with citizens. Developed nations have well thought of strategies to use OSM for policing. However, developing nations like India are exploring and evolving OSM as a policing solution. India, in recent years, experienced many events where rumors and fake content on OSM instigated communal violence. In contrast to traditional media (e.g. television and print media) used by Indian police departments, OSM offers velocity, variety, veracity and large volume of information. These introduce new challenges for police like platforms selection, secure usage strategy, developing trust, handling offensive comments, and security / privacy implication of information shared through OSM. Success of police initiatives on OSM to maintain law and order depends both on their understanding of OSM and citizen's acceptance / participation on these platforms. This study provides multidimensional understanding of behavior, perceptions, interactions, and expectation regarding policing through OSM. First, we examined recent updates from four different police pages- Delhi, Bangalore, Uttar Pradesh and Chennai to comprehend various dimensions of police interaction with citizens on OSM. Second, we conducted 20 interviews with IPS officers (Indian Police Service) and 17 interviews with citizens to understand decision rationales and expectation gaps between two stakeholders (police and citizens); this was followed up with 445 policemen surveys and 204 citizen surveys. We also present differences between police expectations of Indian and police departments in developed countries.