Shares of Tesla tumbled Wednesday following reports US securities regulators have subpoenaed the electric car maker's Chief Executive Elon Musk over his statements about taking the company private.

Shares dropped 3.3 percent to $336.40 in afternoon trading after news of the formal demand for information was released by the New York Times and Fox Business.

The development suggests the oversight by the US Securities and Exchange Commission—which was characterized in previous news articles as an inquiry—has "advanced to a more formal, serious stage," said The Times, which cited a person familiar with the matter.

A subpoena "typically requires the approval of top SEC officials," the newspaper added.

A Tesla spokesperson declined comment.

Musk has been under scrutiny after disclosing a proposal to take the company private on Twitter and saying that financing for a transaction was "secured," a claim that analysts viewed skeptically.

Some Tesla board members were reportedly caught off guard by Musk's tweets and have urged the controversial chief executive to stop using the social media platform.

Tesla's board of directors said Tuesday it formed a special committee to consider the proposal.

Musk on Monday explained in a blog post that his statements about financing were based on his conversations with Saudi Arabia's sovereign wealth fund and other investors.