The officer, identified as Vijendra Bishnoi (33), a native of Rajasthan, allegedly had an extra-marital affair with the woman, Nikita Chauhan, a former news stringer who lived in Dwarka and had separated from her husband, said a senior police official.
Bishnoi, himself was an accused in a domestic violence case registered on the basis of a complaint filed by his wife in Rajasthan, the official said.
According to police, the incident took place around 9.45 AM today when Bishnoi asked the woman to come to the park, where they were last seen sitting on a bench and talking to each other.
Seconds after that, Bishnoi pointed the gun towards himself and fired two rounds.
While one bullet hit his abdomen, the other hit his chest.
Locals called up the police and both were rushed to a hospital, where the woman was declared brought dead and Bishnoi was reported to be in a critical condition.
"He was then moved to AIIMS Trauma Centre where he died in early evening," DCP (Southwest) R A Sanjeev said.
Bishnoi, who is survived by a son and a daughter, was posted at west Delhi's Ranhoula police station.
"A case has been registered under relevant sections of law and investigation is underway," Joint Commissioner of Police (Southwest) Dependra Pathak said.
An official privy to the probe added that from preliminary investigation, it appears that the woman was extorting money from Bishnoi and had even allegedly threatened to frame him in a false case.
However, such allegations are to be subjected to several layers of verification.
During investigation it also emerged that the woman, who had married a man identified as Bittu in 2011, was a news stringer for electronic media (Hindi) and had met Bishnoi during an assignment, but was jobless at least for the past one year, said the official.
Nikita and Bishnoi were also found to have gone for vacations together outside Delhi, the official said, adding that it is also likely that Nikita was being helped by someone in the suspected extortion.
The case is being probed from multiple angles and several persons have been questioned so far, the official added.
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