She filed the complaint on Monday, a day after she sought Kerala Chief Minister Pinarayi Vijayan's help to track down the accused and arrest them.
Ms Nishanth said she has been getting death threats on social media, and even accused one Bharatiya Janata Party leader of sharing her number.
"Attempts of threatening and shaming me has been going on in social media. TG Mohandas has posted my phone number and address on twitter which has created problems for me at a personal level," Ms Nishanth said in her police complaint, seen by NDTV.
TG Mohandas is the convener of BJP's intellectual cell.
"I am told that false complaints have been filed against me at Thrissur police station. Social media groups with explicit content have been carrying my photographs and details, causing much damage to me. Now I am complaining because of death threats against me," the lecturer said.
In the screenshot that Ms Nishanth shared with the police, a man purportedly from Bahrain identified as Ramesh Kumar Nair wrote on Facebook on April 28: "We want her blood as well. She has crossed our limits of patience."
Deepa Nishanth told the police that Biju Nair claims to be a worker of the BJP's information technology cell. "Biju Nair... has given death threats to me from his own Facebook profile page and deleted his comment after public outrage..." the lecturer said in her complaint.
BJP intellectual cell convenor TG Mohandas denied sharing the lecturer's phone number with those who abused and threatened her on social media. "I don't know Deepa Nishanth. I don't have her number. I have only read about her. I did re-tweeted a thread about her, asking for legal action to be pursued against her. That only had her college name. I don't know her beyond that," Mr Mohandas told NDTV.
Ms Nishanth apparently became a target herself after she shared the post of Bengaluru resident Deepak Sanakaranaryanan, who in early April wrote on Facebook that the horrific gang-rape, torture and murder of an eight-year-old girl in Jammu and Kashmir's Kathua was carried out with the consent of "31 per cent of India's voters". The BJP's vote share in the 2014 Lok Sabha election was 31 per cent.
The Thiruvananthapuram police have already filed a case against Mr Sankaranarayanan.