The incident took place in Pandav Nagar late on Sunday night and the deceased has been identified as Saurabh, who was also preparing for civil services, they said.
The police are questioning his female friend, a law graduate from Delhi University, to ascertain details leading to the incident.
However, no case has been registered so far.
According to the police, she told investigators that she returned from a party and saw Saurabh consuming alcohol on the terrace.
They had a brief altercation following which she came downstairs, the police said, quoting her. When she was climbing down the stairs, she heard something falling down and later, found him lying in a pool of blood.
Neighbours rushed to the spot for help and called an ambulance but it did not come. The girl then called a friend who lived in neighbouring Noida.
The police claimed that the incident was reported to them only at around 1 am though the incident took place at 10:30 pm on Sunday night.
Investigators are now looking into the delay in informing police. They were checking whether it was intentional or whether the girl just panicked.