The suit stems from a sexual assault case against Uber in late 2014 in New Delhi. Ms. Doe requested an Uber and was picked up by Shiv Kumar Yadav, a driver for the ride-hailing company. The police said Mr. Yadav diverted from the intended route to Ms. Doe’s home, then switched off his cellphone so he was untraceable. He was later arrested, convicted of kidnapping and sexual assault, and is serving a life sentence.

At the time, Uber executives were publicly contrite, saying in a statement: “Our thoughts are with the victim of this terrible crime, and we are working with the police as they investigate. We will assist them in any way we can.”

Privately, investigators and Uber employees obtained and discussed the woman’s medical records as the case progressed, three people familiar with the matter but who were not authorized to speak publicly about it have said.

How those documents were obtained remains a question. But as The New York Times and others have reported, Uber executives discussed the possibility that the rape could be tied to one of its competitors in India — such as a taxi company or Ola, the largest Indian ride-hailing company — as part of a plan to sabotage Uber’s momentum in the region. One day after the rape was made public, Uber was banned by officials in New Delhi.

In 2015, Ms. Doe withdrew a separate lawsuit against Uber after agreeing to enter private mediation.

The new revelations about Ms. Doe’s medical records have had repercussions. This month, Uber terminated Mr. Alexander, one of the executives who had obtained the medical records. On Monday, Mr. Michael announced he had left the company after the investigation into Uber’s workplace had resulted in a recommendation for his exit.