SAN FRANCISCO—With federal investigators turning their attention to Uber Technologies Inc., there could be busy times ahead for the company's outside lawyers.

On Thursday, the federal judge overseeing the company's intellectual property showdown with Google over driverless car technology referred the case to the U.S. attorney's office “for investigation of possible theft of trade secrets.”

That compounds problems for the ride-hailing company, which is already facing a federal criminal investigation over its use of a software tool to help drivers avoid local transportation regulators, according to news reports.