if live feed is considered then first time orelse they do hire dji services from locals for some events and all surveillance stuff
No, Kolkata police owns this one as well as several others. Its not outsourced. They have a traffic control room at police HQ from where keep watch. Last year they also used a drone in a fire incident on the 15th floor of a building to find out trapped people. That was a much bigger one...not a DJI.
Several government departments have started using drones. Last year a funny incident happened when the agriculture dept. was making a video using a drone. They were filming a market when a farmer threw a cauliflower at it and took down the drone. The drone was recovered but someone took away the camera http://www.rcindia.org/chatter-zone/hilarious-