Separately on Thursday, the National Highway Traffic Safety Administration (NHTSA) opened a formal probe into 416,000 Tesla Model 3 and Model Y vehicles after receiving complaints about unexpected braking tied to its Autopilot system.
Tesla has issued 10 recalls since October, including some under pressure from the NHTSA.
Shares of Tesla closed $47.04, or 5.1%, lower on Thursday to $876.35 on Nasdaq.
The cases are SEC v Musk, U.S. District Court, Southern District of New York, No. 18-08865; and SEC v Tesla Inc in the same court, No. 18-08947.
(Reporting by Jody Godoy and Jonathan Stempel in New York, and David Shepardson in Washington; Editing by Toby Chopra, Mark Porter and Sandra Maler)