Preliminary questioning revealed that it was a fall-out of the woman's refusal to marry the accused, Srinivas.
Both had been shifted to a corporate hospital as they were in a critical condition, said Assistant Commissioner of Police, T Sarath Babu.
Police Constable Srinivas, who was on guard duty, shot Lalitha, a colleague, with his service rifle when the latter was sleeping in the rest room post duty-hours. He then went on to shoot himself in the chest, ACP Babu told PTI.
The bullet hit Lalitha's forehead.
According to Babu, Srinivas said that he shot Lalitha because she had refused to marry him.
Both Srinivas and Lalitha joined the police department in 2009.
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