The taxi driver was critically injured in the incident which took place on Africa Avenue-Church Road crossing in R K Puram at around 3:30 am on Thursday.
Dinesh Tanwar, son of Congress leader Kanwar Singh Tanwar, fled the accident site.
He finally surrendered on Thursday evening. He was arrested for rash and negligent driving but almost immediately was granted bail.
The police claim since many hours had passed since the accident, an alcohol test could not be conducted.
The accident took place at around 3:30 am on Thursday while the driver of the Mercedes car surrendered after almost 18 hours of the incident.
The police now say it is practically impossible to establish whether he was driving under influence of alcohol.
The woman, who was in her 30s, is yet to be identified. The taxi driver, Naresh Kumar, has been admitted to AIIMS Trauma Centre. Police could not record his statement as he was in a critical condition. Tanwar was not available for comments.
The Mercedes has been sent to the Delhi Police forensic lab in Malviya Nagar.
The Mercedes-Benz car belonged to Kanwar Singh Tanwar, who was the richest candidate in Delhi during Lok Sabha elections in 2009 and had fought the polls on a BSP ticket.
Dinesh was returning from a party, police said but added that it was not clear as yet whether he was drunk. "Due to the impact of the collision, the door of the taxi unhinged and the woman was thrown out of the vehicle. She fell into a roadside drain and suffered severe head injuries," the police official said.