The preliminary inquiry report of crime branch sleuths and their technology experts also did not rule out the involvement of more than one person in the murders, it said.
Dinabandhu Mallick, his wife Nirmala, and their two minor daughters, aged 11 and four, were found dead with their throats slit in their house on Tuesday. The state government has entrusted the investigation into the case to crime branch.
While the relatives and friends of Mallick family are being questioned, police are yet to take anybody into custody.
Meanwhile, investigators have collected blood-stained clothes and other material from Mallick's house for examination.
Police suspect that more than two sharp weapons were used to slit the throats of the victims and are looking for the weapons of offence. Since there was no forced entry into the house, police suspect that the assailants were likely known to the family.