Alleging that the police have not gone through the crime details in "the seriousness it deserved", the victim's father said he did not trust the version that his daughter was killed single-handedly by a private security guard who was arrested on Sunday.
The family has now demanded the case be handed over to the Central Bureau of Investigation.
The police claimed to have cracked the case on Sunday and said a private security guard had tried to force himself on the victim and that he killed her with the "keys of his motorcycle" after his attempt failed.
The police earlier said more men than one were involved in the crime and that it was a gang rape.
Sutapa Sanyal, additional director general of police, who headed the probe team, had said at least five-six people appeared to have been involved in the crime.
Victim's father: Don't trust the version given by the police
However, the police had a different story to tell Sunday.
The woman had 16 "serious injuries" on her body, as her autopsy report said. The police theory that these deep wounds, which led to the woman "bleeding to death", were inflicted by a bike key have left many in the force nonplussed.
"This is a sham that is being put forth because there is immense pressure from the Chief Minister's Office to crack the case and put an end to the media scrutiny," confided a senior police official, at the same time questioning the flip-flops in the case.
Questions are also being raised on how the initial police suspicion of gang-rape in the case was changed to a suspicion of rape, and subsequently now to police saying that "nothing of that sort" happened.
There was no sexual intercourse hence rape is ruled out, a police officer told IANS.
Police claim that "it is one-man job" is being questioned.
"There is a dhaba (roadside eatery) and a temple nearby. How can a crime so gruesome be done without anyone coming to know of it?" the victim's family has asked.