The court directed the Mamata Banerjee government to ensure the security of the victim's family, which has expressed fears in the matter.
Hearing a petition filed by the victim's family seeking a probe by the Central Bureau of Investigation (CBI) into the crime, Justice Dipankar Dutta asked the state advocate general to reply in seven days as to why a CBI probe should not be ordered in the case.
"The court has asked the state government why it should not order a CBI inquiry into the case. Once the government submits its reply, the court will decide the future course of action," petitioner's counsel Bikash Ranjan Bhattacharya said.
The court has also directed the state government to ensure the security of the victim's family, which has been living in constant fear," Bhattacharya said.
Contending that state police have not been properly investigating the matter, the victim's family had filed the petition Jan 6, seeking a CBI probe. The matter will come up for hearing next Jan 15.
The girl, hailing from Bihar, was raped twice by a gang in October in Madhyamgram of North 24-Parganas district. She breathed her last Dec 31 at the state-run R.G. Kar Medical College and Hospital, where she was admitted with severe burn injuries Dec 23.
The case has attracted severe criticism after the family alleged that the police tried to forcibly cremate the body of the victim, and has also been threatening the family, seeking that it leaves the state.
The family members Tuesday met President Pranab Mukherjee and demanded death for the guilty.