Seema Singh, the mother of Sara, wrote a letter to Senior Superintendent of Police, Lucknow, and asked for registration of an FIR.
"I suspect my daughter was killed as part of a conspiracy and did not die in an accident. I request you to lodge an FIR in this matter and initiate probe," Sara's mother Seema Singh said in the letter.
Sara (27) died when the car in which she was travelling overturned in a pit in a bid to save a cyclist in Firozabad district on July 9.
The family of Sara had earlier demanded Narco-analysis test of Amanmani.
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"Some findings in the post mortem report of Sara raise doubts over her death and a narco analysis test on Amanmani can answer a lot of questions," 27-year-old Sara's mother Seema had said.
Earlier, on July 13 Seema and his son had met Director General of Police Jagmohan Yadav and gave an application for CBI inquiry into the death of her daughter.
Amanmani had been evading arrest in connection with a kidnapping and loot case and was arrested after the accident.
Amarmani was arrested in September 2003 in connection with
the murder of poet Madhumita Shukla, with whom he allegedly had an affair. Madhumita was murdered on May 9, 2003.
The post mortem report of Madhumita revealed that she was carrying a foetus that matched the DNA of Amarmani and he and his wife Madhumani were sentenced to life imprisonment in October 2007.