A policeman allegedly fired several rounds outside the Bangladesh Deputy High Commission in central Kolkata's busy Park Circus area on Friday afternoon, killing a woman before shooting himself dead, police said.

The woman, who was riding pillion on a two-wheeler, fell down after being hit by a bullet as the on-duty policeman kept firing from his rifle, triggering chaos in the congested area, they said.

She died on the spot, while the policeman after firing a few rounds more shot himself in the head, they added.

The identities of the woman and the policeman are yet to be known.

"The whole episode lasted for around five minutes," said a visibly shaken Bablu Sheikh, who claimed to have witnessed the incident.

A huge contingent of police reached the area minutes later and took away the bodies.

Preliminary investigations are underway, police said.