SAN FRANCISCO (Reuters) - The U.S. judge overseeing a blockbuster case over self-driving car technology suggested Uber could face an injunction if a key Uber executive does not testify for fear of exposing himself to criminal prosecution, according to a transcript seen by Reuters.

The Waymo logo is displayed during the company's unveil of a self-driving Chrysler Pacifica minivan during the North American International Auto Show in Detroit, Michigan, U.S., January 8, 2017. REUTERS/Brendan McDermid

Waymo, the self-driving car unit of Alphabet Inc GOOGL.O, sued ride services company Uber Technologies Inc [UBER.UL] last month, alleging that a former Waymo executive, Anthony Levandowski, downloaded over 14,000 confidential documents before leaving the company to subsequently join Uber. Waymo said Uber benefited from those documents.

Levandowski is not a defendant in the case, but he is a central figure in the high-profile litigation that pits two Silicon Valley technology giants against each other, both of which are vying to dominate in the competitive autonomous vehicles sector.

Waymo is seeking a preliminary injunction from the court, which would temporarily stop Uber from using any of the allegedly stolen intellectual property. A hearing is scheduled for May 3.

Uber, which has said the allegations are baseless but has not yet responded to Waymo’s complaint in court, has argued that the trade secrets issue should be sent to arbitration.

“You represent somebody who’s in a mess,” U.S. District Court Judge William Alsup in San Francisco told the attorney for Levandowski, Miles Ehrlich, during a closed court hearing on Wednesday. Reuters saw the transcript of that hearing.

Ehrlich had told the court that based on the “potential for criminal action” against Levandowski, the engineer would be asserting his Fifth Amendment rights against self-incrimination.

Contacted on Thursday, Ehrlich denied further comment. Uber did not respond to a request for comment.

‘GOOD STORY TO TELL’

In the hearing, Alsup bandied with lawyers for Uber and Levandowski over the allegedly stolen documents, some of which Uber said were not in its possession, but in Levandowski’s.

Gonzalez said he would like to put Levandowski on the stand, because “he has a good story to tell,” but could not force him. But were the case sent to arbitration, Levandowski might choose to testify, Gonzalez said, because arbitration proceedings are not public.

“At least it’s not in the public where it’s going to be in the front page of The New York Times the next day,” Gonzalez said, an argument rejected by the court, which said the public had a right to know details of the case.

“I’m sorry that Mr. Levandowski has got his -- got himself in a fix. That’s what happens, I guess, when you download 14,000 documents and take them, if he did. But I don’t hear anybody denying that,” Alsup said.

Gonzalez suggested Uber’s strategy would be to convince the court that Uber was “not using any of these things” Waymo says he stole.

“That would be a legitimate point,” responded Alsup. “Maybe you can convince me of that.”

Still, Alsup warned Uber of its difficulty in dodging a preliminary injunction in light of Levandowski’s Fifth Amendment privilege.

“If you think for a moment that I’m going to stay my hand because your guy is taking the Fifth Amendment and not issue a preliminary injunction to shut down that ... you’re wrong,” Alsup said.