By David Shepardson

WASHINGTON (Reuters) - The fatal Dec. 29 crash of a Tesla Inc vehicle in Southern California will be investigated by the U.S. government's auto safety regulator, the agency said on Tuesday.

The U.S. National Highway Traffic Safety Administration (NHTSA) said earlier this month it had opened an investigation into a 12th Tesla crash that may be tied to the vehicle’s advanced Autopilot driver assistance system after a Tesla Model 3 rear-ended a parked police car in Connecticut.

NHTSA did not say if autopilot was suspected in Sunday's crash in Gardena in Los Angeles county.

Tesla did not immediately respond to a request for comment.

Los Angeles television station KTLA reported the driver exited the 91 Freeway in Gardena, ran a red light and struck a 2006 Honda Civic, killing its two occupants.

The two people inside the Tesla were hospitalized but did not have life-threatening injuries, KTLA reported, citing Los Angeles police.

Autopilot had been engaged in at least three Tesla vehicles that were involved in fatal U.S. crashes since 2016. The National Transportation Safety Board has criticized Autopilot's lack of safeguards and said in September in its probe of a 2018 Culver City, California Tesla crash that the system’s design "permitted the driver to disengage from the driving task."

Tesla and NHTSA both advise drivers that they must keep their hands on the steering wheel and pay attention at all times while using Autopilot. Tesla says Autopilot "enables your car to steer, accelerate and brake automatically within its lane," but does not make the vehicle autonomous.

Some drivers say they are able to keep their hands off the wheel for extended periods when using the system. Last month, U.S. Senator Ed Markey said Tesla should disable Autopilot until it installs new safeguards to prevent drivers from evading system limits that could let them fall asleep.

NHTSA has previously confirmed special crash investigations in a number of Tesla crashes but until earlier this month had not disclosed the total number of crashes under review. NHTSA previously investigated another Tesla crash that it initially suspected of being tied to Autopilot but ruled it out.

(Reporting by David Shepardson; Editing by Leslie Adler and Grant McCool)