SAN FRANCISCO—During a Wednesday court hearing, a federal judge said that if an Uber engineer accused of a massive data theft from his former employer is going to invoke his Fifth Amendment right to protect against self-incrimination and not hand over materials demanded as part of a recent subpoena and upcoming deposition, then he must at least explain himself privately to the judge.

“What I’ve told you is that you can submit the privilege log to me, in camera, without giving it to anyone else and I can evaluate it, which aspects, if any would be incriminating,” US District Judge William Alsup said, addressing a lawyer representing the engineer, Anthony Levandowski, during the hearing. “I’m not ruling against the ultimate assertion of the privilege, but you’ve got to do more than just say in court, Fifth Amendment—you have to do a privilege log and go through the process.”

The case pits Waymo against Uber, which in turn is in a tense situation with one of its own employees, Levandowski, the head of its self-driving division.