27-year-old Anton Yelchin was found pinned between his 2015 Jeep Grand Cherokee and a fence at his home in Los Angeles.
The LAPD says the SUV was on and rolled into the Star Trek star because he may not have put it into park Properly.
It's too early in the investigation to know if and issue with the vehicle's computerized shifter played into the deadly accident.
The monostable electronic gearshift, or E-shift, lacks the typical grooves and sensation of moving the car into park, drive, or reverse.
And there have been more than 600 complaints about the vehicles not properly going into park, and in some cases, rolling away.
In April Fiat Chrysler voluntarily recalled 1.1 million vehicles including the 2014 and 2015 Jeep Grand Cherokees.
But company documents show the fix wasn't expected to be offered until at least July.
CBS News first reported about this in March.
Gary Titus told us about issues with his 2014 2014 Jeep Grand Cherokee.
I got out of the jeep, I thought it was in park, and it was in reverse still.
We drove a similar vehicle at the consumer reports test track in Connecticut.
Here, I pushed all the way foreword.
Necessarily mean I end up in park.
In a statement, Fiat Chrysler says, "FCA US extends its most sincere condolences to the family and friends of Mr.
The company is in contact with the authorities and is conducting a thorough investigation." Kris Van Cleave, CBS News, Washington.