The women students jumped into a well at the medical college on Saturday.
They left a suicide note blaming the college authorities for charging excessive fees and not providing receipts.
Students of the college and their parents have held protests demanding action against the authorities.
Police have arrested the son of the owner of the college as well as the principal and charged them with extortion, cheating and abetting suicide.
In their suicide note E Saranya, V Priyanka, both 18, and Monisha, 19, of the SVS Yoga Medical College, also alleged that despite charging prohibitive fees, the college lacked proper classes or teachers and there was "nothing to learn".
A senior police official told the BBC Hindi's Imran Qureshi that they were searching for the owner of the college Vasuki Subramanian.
A newspaper report said the medical college is "without classrooms, laboratories and teachers for around 100 students, who were charged at least 500,000 rupees ($7,382; Â£51,70) each in fees alone - and not a single placement conducted on campus since the beginning in 2008".
Another Indian news report said the "mortuary once doubled up as a dining hall, and the operation theatre is really a dirty room with three cots".
Reports say there were a number of protests last year by students against "excessive fees" charged by the college, but little action was taken.
Police in India's Tamil Nadu state have arrested two people after three students of a private medical college took their lives citing excessive fees.