Video footage filmed by Dakota Randall appeared to show the driver and his front-seat passenger napping as they travelled down the Massachusetts Turnpike toll road in Boston on Sunday afternoon.
Posting the video on Twitter, the sports journalist wrote: “Some guy literally asleep at the wheel on the Mass Pike (great place for it). Teslas are sick, I guess?”
Mr Randall estimated the Tesla was travelling at about 60mph on the 138-mile-long road as he drove alongside it for about a minute.
He told NBC Boston: “I kind of looked over and saw what I thought was somebody asleep at the wheel and I was like that can’t be right, so I did a double take, looked over and sure enough this guy was just head between his legs completely asleep.”
Mr Randall said he sounded his horn at the car, but the driver still did not wake up.
His video attracted scepticism from some Twitter users, who suggested the driver and his passenger may have just been pretending to be asleep, while others branded the footage “fake”.
Responding to the tweets, Mr Randall said: “For the record, this was no hoax, at least not on my part. Maybe the people in the car were faking being asleep, but I’m sceptical.”
Tesla’s auto-pilot feature allows the vehicle to steer, accelerate and brake automatically in a single lane.
However, the company’s website insists the feature still requires “active driver supervision” and does not make the car autonomous.
A spokesperson for Tesla told The Independent: “Many of these videos appear to be dangerous pranks or hoaxes.
“Our driver-monitoring system repeatedly reminds drivers to remain engaged and prohibits the use of Autopilot when warnings are ignored.
“At highway speeds, drivers typically receive warnings every 30 seconds or less if their hands aren’t detected on the wheel.”
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