India's top anti-crime agency is taking over the investigation into the death of actor Sushant Singh Rajput, whose suicide has shaken Bollywood and sparked bitter recriminations.

Rajput, 34, was found dead in June in his Mumbai apartment - with police saying he took his own life - setting off a debate over mental health in the multibillion-dollar industry.

His former girlfriend, fellow actress Rhea Chakraborty, petitioned the Supreme Court on Wednesday after Rajput's family disputed reports that he suffered from depression and accused her of stealing his money and harassing him.

Chakraborty strongly denied the allegations and asked the country's highest court to transfer the case from local police in Rajput's home state of Bihar.

Government solicitor general Tushar Mehta told the hearing the Central Bureau of Investigation, India's top federal crime agency, would take charge of the case, which has grabbed media headlines for weeks.

Born in eastern Bihar state, Rajput quit engineering studies to pursue a career in acting and dance.

He got his big break in 2013 with Kai Po Che, a film about cricket, love, and politics that won acclaim at the Berlin film festival.

He was also lauded for his portrayal of Indian cricket hero Mahendra Singh Dhoni in the 2016 hit, MS Dhoni: The Untold Story.

In an interview with AFP in 2016, Rajput spoke of the emotional rollercoaster he experienced while filming the movie, which portrayed the heartbreak suffered by Dhoni when the cricketer's girlfriend died.

Rajput's death - barely a week after his manager took her own life - rekindled discussions about mental health in the industry.

Stars such as Deepika Padukone and Anushka Sharma, who have spoken about their own battles with depression and anxiety, posted messages about the importance of seeking help.

It also sparked an angry outcry from fans and fellow actors about the difficulties faced by aspirants struggling to grab a foothold in Bollywood, with some attacking the industry for its insiders-only culture.

Although many of Bollywood's top stars such as Shah Rukh Khan and Priyanka Chopra Jonas do not hail from film families, the industry has a long history of offering leading roles to the children of celebrities, often with no prior acting experience.