In the video, the student, said to be Gowtham Sudarshan, a final year MBBS student of a private medical college, is seen dropping the dog from the terrace of a building which appears to be a three-storeyed structure, police said.
He looks into the camera, lifts the dog by holding on to its skin and drops it after getting the animal onto the parapet wall.
The shocking act was captured on camera by his friend, said to be Ashish Pal, who has also been named for abetting the crime in the complaint, police said.
"When we saw the video, we were shocked. It was a barbaric act and the perpetrator and abettor must be punished by law," animal welfare activist Antony Clement Rubin, who lodged the complaint along with other activists said.
Kundrathur Police confirmed that an FIR was registered against Gowtham Sudarshan and Ashish Pal under provisions of IPC and Prevention of Cruelty to Animals Act adding they are on the look out for the accused.