Superintendent of police S M H Mirza today said the 32 year-old youth, employed by a private telecom company, had entered the girl's house at Eta village with a pistol last night.
Finding the girl sleeping with her mother, he shot her in her hand and hips injuring her critically.
Hearing the noise of the firing, the girl's father rushed into the room and was shot at fatally in his forehead and heart and he died on the spot, Mirza said.
Neighbours rushed out and caught the youth who tried to train the pistol on himself and commit suicide. His pistol was, however, snatched away and he was lynched.
The girl was later rushed to hospital, where her condition was stated to be critical.
Mirza said the girl, an undergraduate, had been in a relationship with the youth, who is a resident of a near-by village for the past three years but had stopped communications with him since March.
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Some letters written by her and some photos of her and the youth were found on the person of the youth.
Police registered two FIRs in connection with the incident.