The incident occurred in Bhupalapally, the headquarters of Jayashankar-Bhupalapally district in Telangana, on Wednesday night.
According to police, 22-year-old Ganesh committed the offence when his maternal cousin Sandhya Rani, 19, was alone at her home.
The youth, who had been pestering her to marry her, suspected she was in love with another cousin. During a heated argument over this, Ganesh repeatedly stabbed her with a kitchen knife.
On hearing the cries of the girl, neighbours rushed to the house.
While the girl died on the spot, Ganesh escaped. He went on to the terrace of an adjoining building and jumped on the high-tension power lines.
The youth’s body was removed by the police with the help of rescue team of Singareni Collieries Co.
Ganesh, who hails from Paloncha town in Khammam district, had come to Bhupalapally three days ago and was staying at his maternal uncle’s house.
Sandhya was a student of second year of graduation in a college.