The incident took place on Wednesday evening when the constable identified as Anil, posted in east Delhi's Khajuri Khas police station, jumped off the Yamuna Bazar flyover near Kashmere Gate in north Delhi.
"He was seen travelling in an auto-rickshaw with two friends, including a woman, minutes before he took the extreme step," said a police official.
When the auto-rickshaw reached the middle of the flyover Anil asked the driver to stop.
His companions made a PCR call following the incident.
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A huge crowd had gathered at the spot.
A PCR rushed him to the Bara Hindu Rao Hospital where his condition is said to be critical.
Police is unable to understand the exact cause behind his suicide bid "as no suicide note has been recovered from him", he added.
He is not fit for statement, we will be able to know the reason behind the extreme step only after he is able to speak, the official said.