Anitha, 17-year-old Dalit girl who was the face of the fight against NEET, took her life on September 1.
The plea also wants the Tamil Nadu Government to maintain law and order and ensure that protests over Anitha's death don't disrupt normal life.
The PIL has demanded a judicial inquiry by retired High Court judge.
A day after the suicide protests were held across Chennai on September 2 by many groups, including the Left parties and PMK.
The protestors blamed both the State and the Central Government for Anitha's death. (ANI)