Bruce Jenner -- Cops To Get Search Warrant for Cellphone -- Was He Texting?

The L.A. County Sheriff's Dept. will get a search warrant to determine if Bruce Jenner was texting at the time he slammed into a car, causing the driver to die ... TMZ has learned.

Law enforcement sources tell TMZ, they will get warrants for both Bruce's phone records and the cellphone itself. It's illegal to text while driving in California and if Bruce was texting Saturday when he struck a car on PCH in Malibu, authorities could charge him with vehicular manslaughter.

The photos we posted showing Bruce in the car immediately before impact do not reveal what if anything he's holding. It appears he might be clutching something in his left hand but it's unclear.

Even if he was texting, our sources say proving he was doing it at exactly the moment of the crash could be difficult or even impossible.

Our law enforcement sources also tell us they're positive Bruce tried to avoid the accident. The tires on his trailer produced significant skid marks and at the last minute Bruce veered to the right, causing the Lexus to swing left into oncoming traffic. A Hummer struck the Lexus, killing the Lexus driver.

We're told cops are skeptical about the story of the Prius driver, who was hit from the rear by the Lexus in the chain reaction. The Prius driver says she was stopped at a red light, but she was about 300 feet from the light itself. Cops don't know if there was a long line of cars in front of her or if she stopped before the light to make an illegal U-turn. They tell us her story is "vague."

We're told cops didn't check Bruce's phone at the accident scene. As one law enforcement source put it, "We were more interested in his sobriety." Bruce passed the sobriety test.