The women had jumped into a well near their college leaving behind a note that blamed the institution's chairperson and management, the police has said.
The young women were undergraduate students of SVS Medical College of Naturopathy and Yoga Sciences in Villupuram, about 200 km from Chennai.
They have been identified as second year students V Priyanka, T Monisha and E Saranya. They allegedly tied themselves together with a dupatta (scarf) and jumped into a farm well near the college.
Police claim to have recovered a suicide note which allegedly blames the college management and in particular it's chairperson.
They have registered cases of extortion, cheating and abetting suicide.
A senior police officer told NDTV that their letter talks about "extortion by the management and how students are fighting for even basic amenities".
The bodies were retrieved by police and fire brigade personnel and sent to a government hospital for autopsy, police said.
Anxiety and tension prevailed in the area as residents, students and parents gathered at the spot of the incident.
District Superintendent of Police Narendra Nair said, "We have not made any arrests yet. We are investigating."
Family members of the students say the girls were harassed by the college management.
"It is a murder, not a suicide. We want a post-mortem done in Chennai, not a Villupuram hospital," said the father of one of the girls.
A relative of another student said, "The college management harassed and tortured students."
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