In their letter to the CM, they have alleged that Pratyusha's boyfriend and actor-producer Rahul Raj Singh was "solely responsible for her death".
"...she fell prey to conman Rahul Raj Singh, who has not only cheated my daughter and is solely responsible for death, but also cheated many innocent girls like her to the tune of lakhs of rupees," said the letter, dated April 13, signed by Pratyusha's mother Soma Banerjee.
The letter, which has also been addressed to Minister of State for (Home) Ranjit Patil, Mumbai Police Commissioner Dattatray Padsalgikar and Joint Commissioner of Police (Law and Order) Deven Bharti, alleged that their complaint was not being heard by police.
The actress' mother alleged that instead of seriously investigating the matter, the Bangur Nagar police, where the case has been registered, was giving a free hand to the accused to destroy the evidence.
"He (Rahul) also has been threatening us and the witnesses. The death of my daughter is being coloured and portrayed as a suicide committed due to depression," it stated.
"Our appeal to you is that the investigation in the case should be transferred to Mumbai Crime Branch for a fair investigation so that justice is done after our daughter's untimely and mysterious death," the letter further said.
The 'Balika Badhu' fame actress was found hanging at her residence in Goregaon on April 1. She was then rushed by Rahul to a hospital in Andheri where she was declared dead.
Rahul, who has been booked for abetment of suicide, has been undergoing treatment for alleged depression at a hospital in Borivali since April 3.
The Bombay High Court had on Tuesday granted Rahul interim protection from arrest till April 18.