Two US consumer rights groups have urged the Federal Trade Commission to investigate Tesla over its marketing of "Autopilot" assisted-driving software.
In a letter sent on Wednesday, the groups called the Autopilot name "deceptive and misleading".
A small number of drivers using the software have been involved in crashes.
Tesla says customer feedback shows "a very clear understanding of what Autopilot is, how to properly use it and what features it consists of".
Tesla instructs drivers to keep both hands on the wheel and eyes on the road while driving using Autopilot.
In the letter, The Center for Auto Safety and Consumer Watchdog say: "The marketing and advertising practices of Tesla, combined with Elon Musk's public statements, have made it reasonable for Tesla owners to believe, and act on that belief, that a Tesla with Autopilot is an autonomous vehicle capable of 'self-driving'".
After a fatal crash in Florida, the National Transportation Safety Board determined that the "driver's inattention due to over-reliance on vehicle automation" was a probable cause.
The board found that the driver's usage of the system "indicated an over-reliance on the automation and a lack of understanding of the system limitations".
In Britain, a driver was banned from driving after putting his Tesla in Autopilot on the M1 and sitting in the passenger seat.
Bhavesh Patel told St Albans Crown Court that he was the "unlucky one who got caught".