The woman made a complaint at Mountjoy Garda station on December 9, but because of where the sexual assaults were originally alleged to have taken place, the case is being investigated by officers from Irishtown Garda Station.
The 22-year-old was taken to the Sexual Assault Treatment Unit at the Rotunda Hospital where examinations confirmed that she had been brutally sexually assaulted.
However, the chief suspect in the case has denied he raped the alleged victim.
Gardai say that a "protracted investigation" will now need to take place in light of the suspect's denial.
Witnesses came forward after investigating gardai issued an appeal for people who may have seen her in the Mountjoy Square area in the immediate aftermath of her ordeal.
The witnesses told gardai that she was in a very distressed state. A senior source said the woman was raped three times in the vehicle between 12.43am and 2.14am.
The woman had attended a Christmas party in a Ballsbridge hotel the night before.
She told detectives she hailed a taxi from the venue, but got out of the car in the Shelbourne Road area after she became unwell. She believes she got into another taxi in the Dublin 4 area and officers think she was raped in this vehicle and ended up in Mountjoy Square.
Officers yesterday announced details of the arrest of the taxi driver who was questioned for a number of hours at Irishtown Garda Station last Thursday before being released without charge the next day.
A file on the case will be now be sent to the Director of Public Prosecutions but sources say the man claims that he did not rape the woman but had consensual sex with her.
After he fled Ireland in the aftermath of the rape, gardai raided his Tallaght home and carried out forensic examinations of the property.
It was reported yesterday that the suspect was abroad but it later emerged that gardai had arrested him when he arrived back in the country.
The taxi in which the woman was attacked in the early hours of December 9 has also been located, seized and forensically examined by officers.
The victim suffered most of her ordeal while the taxi she was in was parked at Emmet Street in Dublin's north inner city.