Ousted Uber CEO Travis Kalanick may have known a star engineer possessed trade secrets stolen from Google, according to a recent court filing.

The court case centers on Waymo, the self-driving car unit of Google-parent Alphabet, and Anthony Levandowski, an engineer who left Waymo to start his own company, Otto, that was later acquired by Uber.

Waymo alleges Levandowski took 14,000 documents with him, including trade secrets. Waymo attorneys filings released this week suggest that Kalanick knew Levandowski possessed, and later destroyed, some of the information in question:

On or about March 11, 2016, Mr. Levandowski reported to [Travis] Kalanick, Nina Qi and Cameron Poetzscher at Uber as well as Lior Ron that he had identified five discs in his possession containing Google information. Mr. Kalanick conveyed to Mr. Levandowski in response that Mr. Levandowski should not bring any Google information into Uber and that Uber did not want any Google information. Shortly thereafter, Mr. Levandowski communicated to Uber that he had destroyed the discs.

Levandowski has exercised his Fifth Amendment rights and has largely been silent on what is in his possession. But a judge told Uber to use "the full extent of their corporate, employment, contractual and other authority" to compel Levandowski to return the documents by May 31. When Levandowski didn't deliver, he was fired.

New filings this week, though, indicate that Uber may have had access to those files earlier, and allowed them to be destroyed prior to the deadline. The information, previously unearthed by TechCrunch, sheds more doubt on the already murky relationship between Levandowski and his former employers at Uber.

"No statement of any destruction was provided pursuant to the Court's Order by the March 31 deadline," Waymo's lawyers wrote in a motion. "Yet, over two months later, Defendants Uber's and [Otto's] June 5 response to Waymo's expedited interrogatory revealed that documents were destroyed, allegedly at Uber's direction, back in March 2016."

The timeline of when Levandowski ended his tenure at Waymo and began negotiating with Uber has become central to the case.

Levandowski collected $120 million from Google, despite involvement with at least one start-up that would ultimately compete with the company, the case alleges. Waymo's lawyers said Levandowski was already trying to staff up his competing start-up, Otto, while he worked at Google — but he waited until he got his payout to make the details of Otto public.

Kalanick and Levandowski's attorney did not immediately respond to CNBC requests for comment. Uber declined to comment.

It all comes amid a rocky time within Uber, after reports of sexual harassment and gender bias led to an into workplace culture. The company is also without top leadership now that Kalanick has resigned in the face of an investor revolt.

"This is certainly a part of the workplace culture: toe stepping, don't be afraid to get in people's faces," Kate Bischoff of tHRive Law & Consulting told CNBC last week. "'Oh, we should hire the guy from Waymo' — that's not something outside the realm of possibility when you've created a culture that wants to ride the line."

The dispute between Waymo and Uber is playing out in two different arenas: In addition to the civil court case, the case has also been referred to the U.S. attorney for investigation of the possible theft of trade secrets.

"There are a whole host of variables that the government takes into account," Phil Bezanson, white collar partner at Bracewell, said last week. "Corporate culture is one, tone at the top, pervasiveness of wrongdoing, how the company responded. Because we have so many different subject matter issues, an overall corporate culture assessment is a good thing. The DOJ will pay close attention to it."