The early stage investigation comes after Tesla didn't notify investors of a fatal crash involving its Autopilot function, an unnamed source told the Journal.
A spokesperson for the electric vehicle maker told CNBC that Tesla has not received any communication from the SEC regarding the information in the Journal report.
The May 7 crash first came to light after the National Highway Traffic Safety Administration announced a preliminary investigation.
The crash, when a tractor trailer drove across a divided highway where a Tesla Model S was driving in autopilot mode, resulted in the death of driver Joshua Brown, the Journal reported. It was the first known fatality where Autopilot was activated, Tesla has said.
Earlier this month, Fortune magazine emailed Tesla CEO Elon Musk about whether the company disclosed the crash before an offering of $2 billion in Tesla stock on May 18. He responded it was "not material to the value of Tesla." The company then responded in a longer post, calling the Fortune article "misleading" and "fundamentally incorrect:"
Given the fact that the 'better-than-human' threshold had been crossed and robustly validated internally, news of a statistical inevitability did not materially change any statements previously made about the Autopilot system, its capabilities, or net impact on roadway safety.
Shares of Tesla were down more than 1 percent after-hours trading Monday. The SEC declined to comment to CNBC.
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