Home Minister RR Patil made the announcement in the state Assembly.
Three girls - aged 11, 8 and 6 years - went missing from their house on February 14 and their bodies were found in a well two days later. Initially, there were allegations of rape and the case has not been solved by cops so far.
Leader of Opposition Eknath Khadse, Devendra Phadanvis, Nana Patole (BJP), Ashish Jaiswal (Shiv Sena) and others asked as to why the post-mortem was conducted 17 hours after the bodies were fished out.
"The bodies were kept in the morgue and left to rot," Mr Phadanvis said.
Mr Patil said the delay was because family members were not allowed by villagers to go to Bhandara civil hospital for the inquest. "The family came to the hospital only after police persuaded them," the Home Minister said.
An inquiry will be conducted as to why they were stopped from going to hospital, he said.
"If the family tells the government it is unhappy with the investigation, I would hand over the case to CBI," he said.
To this, Mr Khadse said he had a letter of the victims' mother to Chief Minister Prithviraj Chavan, dated March 2, which said that as cops had failed to crack the case, it be handed over to the CBI.
He further alleged that police were pressurising their mother to withdraw the letter, which is why she was demanding protection.
On this, Mr Patil announced that the case would be handed over to the CBI.