Uttar Pradesh Director General of Police O.P. Singh had said earlier in the day that the government would readily recommend a CBI probe if the family wanted.
One of the deceased, Pushpa Singh, was a witness in the rape case against BJP MLA Kuldeep Sengar.
ADG Rajiv Krishna told reporters on Monday that the state government had decided to bear the entire cost of treatment of the rape survivor and her lawyer who are presently on life support system at the Trauma Centre in Lucknow.
The ADG said that, prima facie, there was no security lapse. He said that the rape survivor had been given nine security personnel, six of whom were stationed in Delhi where she lives.
"We have spoken to the three of the security personnel and they said that the rape survivor had asked them to stay back because there was no space in the car," he said.
Swati Maliwal, chairperson of the Delhi Women's Commission, met the family of the rape survivor at the Trauma Centre on Monday morning.
She told reporters, "The condition of the girl and her lawyer is very critical. The family wants that they should be taken to Delhi in an air ambulance. We are prepared to take the responsibility and I will talk to the concerned officials."
The accident, meanwhile, is taking a political overtone with the Samajwadi Party, Congress and the BSP seeking a CBI probe into the same.
Congress General Secretary Priyanka Gandhi Vadra has raised questions after the Unnao rape survivor's accident.
Reacting to the accident, Priyanka Gandhi took to Twitter, calling the accident "shocking". She demanded to know the progress of the CBI probe into the rape case and also slammed BJP for not expelling accused party MLA Kuldeep Singh Sengar.
BSP President Mayawati alleged that the accident was a conspiracy to kill the rape survivor.
Samajwadi Party President Akhilesh Yadav and the Congress have sought the Central Bureau of Investigation probe into the incident. Akhilesh Yadav questioned the absence of any security personnel at the time of the accident. A CBI inquiry was needed to probe whether it was a conspiracy to eliminate the family or just an accident, he said.
A delegation of Congress and SP leaders also visited the Trauma Centre and met the family members of the survivor.
( With inputs from IANS )