In its letter, the S.E.C. also questioned whether Mr. Musk was truly a “passive” investor, given that he had already publicly criticized Twitter’s content moderation policies and tweeted recommendations about how the social media company should be changed.
Filing as a “passive investor” while secretly planning to take over a company is “fraudulent,” some legal experts have said. Such cases are rarely prosecuted and are difficult to prove, they have added.
The S.E.C. declined to comment. Mr. Musk did not respond to a request for comment. An attorney for Mr. Musk declined to comment.
The Federal Trade Commission is also looking into whether Mr. Musk violated disclosure requirements by failing to notify the agency of his sizable stake in Twitter. Investors typically must notify antitrust regulators of large share purchases to give government officials 30 days to review the transaction for competition violations.
Mr. Musk, who is also the chief executive of the electric car company Tesla and the rocket maker SpaceX, has previously tangled with the S.E.C. He faced an investigation from the regulator in 2018 when he announced on Twitter that he planned to take Tesla private and that he had secured financing for the deal.