Disha Salian, who had worked with the late Bollywood actor Sushant Singh Rajput for some time, jumped off a high-rise in suburban Malad on June 8.
An accidental death report (ADR) was registered in connection with the celebrity manager's suicide at the Malvani police station.
Last week, Salian's family told the police they do not suspect any foul play in her death.
Satish Salian, the father of Disha Salian, said he does not suspect any foul play in her death and is "completely satisfied" with the probe being conducted by the police in the case, an official had said.
In a letter sent to the assistant commissioner of police (ACP), Malvani, Satish Salian alleged that media persons were harassing his family by repeatedly questioning their faith in the police and their way of inquiry, he had said.
Now, in a latest set of developments, Salian has filed a written complaint against three people for spreading rumours about his daughter's death.
According to a report by India Today, Mumbai Police is likely to file an FIR against television actor Puneet Vasishtha, Sandeep Malani and Naman Sharma.
Salian has accused the trio of spreading negative rumours about Disha, which have hurt them.
Last week, many rumours had gone abuzz claiming that Salian's body was found naked. A minister even claimed that she was raped before she died. The cops have rubbished the rumours of her naked body and rape claims. The autopsy report claimed that Salian died of multiple injuries to her head and other parts of the body.
The police are recording statements of neighbours, and are closely monitoring the CCTV camera footage to ascertain any foul play.
Earlier this month, Salian's father wrote to the Mumbai Police, complaining about misleading media reports and false rumours.