Before the U.S. attorney’s office decided against charging a car service driver with raping a customer, D.C. police had obtained an arrest warrant approved by a prosecutor and a judge, according to law enforcement authorities and court records.

But officials won’t say what happened between the time the driver was arrested Wednesday, publicly named a suspect by police Thursday morning and freed from jail by prosecutors later in the evening.

“In this particular case, a warrant was signed by our office,” said Bill Miller, a spokesman for the U.S. attorney’s office. “Upon further review of the case, we determined that additional investigation was needed.”

D.C. Assistant Police Chief Peter Newsham said the warrant’s approval shows that both prosecutors and police had initially agreed on the strengths of the case. Speaking of prosecutors, he said in an e-mail: “As you know, the standard of proof is different for them. . . . We all believed we had a case.”

The incident began in the early morning of Dec. 8 when a 20-year-old woman — who police said had consumed three vodka drinks and shared a marijuana cigarette at a U Street bar — contacted Uber, which connects people to car services as an alternative to traditional taxis.

According to a court affidavit supporting the arrest warrant, the woman told police the driver made suggestive comments to her in the car, and upon arriving at her home in Cleveland Park, grabbed her from behind as she walked up her driveway. The woman told police she fell, hit her head against the sidewalk and was raped.

According to the warrant application, made public Friday, the driver told detectives that the two had oral sex but that it was consensual and that the woman initiated it. He denied having intercourse. He said he carried the woman partly up the driveway and watched her enter her house.

According to the arrest warrant, semen found in the woman’s genitals matched the driver’s DNA. The arrest warrant was approved in February. Police waited until the driver returned to the District from North Carolina to arrest him.

The affidavit also says that a video from a surveillance camera captured part of the driveway and shows the woman “emerge into view along the side of the garage walking to the side door of her home and appears to show [her] wave to the male subject as he walks back down the driveway.”

The woman could not be reached for comment Friday. The driver declined to comment and referred questions to his attorney, who did not return phone calls.

Clarence Williams and James Arkin contributed to this report.