John Elway Golf Cart Tragedy 'Appears To Be A Horrific Accident,' Sheriff Says

2:10 PM PT -- The Riverside County Sheriff's Department just released a statement to TMZ Sports ... saying, "We have not completed our investigation but at this point there is nothing to indicate that this is anything more than a tragic accident."

We've also learned RCSO investigators have not yet spoken to everyone who was riding on the golf cart the evening Jeff Sperbeck tragically fell off of it.

The Riverside County Sheriff says the golf cart incident that resulted in the death of Jeff Sperbeck -- one of John Elway's close friends -- "appears to be a horrific accident."

The tragedy occurred last Saturday just outside of the Stagecoach music festival in La Quinta, Calif. ... and on Friday, after days of probing into the matter, Sheriff Chad Bianco told The Denver Post he and his team of investigators have thus far found no reasons to believe any criminal activity occurred.

Bianco said initially his department didn't even launch an investigation into the incident because none of the medical personnel who raced to the scene suspected wrongdoing.

Bianco said witness statements all lined up, the golf cart showed no signs of malfunctions ... and Elway displayed no indications of being intoxicated.

"It is common practice for medical personnel, whether it be an ambulance personnel or hospital personnel or even fire personnel, to call us after the scene of an accident because something doesn’t look right," Bianco said. "And this was not the case."

While an investigation is still ongoing -- surveillance video is being reviewed as are witness statements -- Bianco said he's anticipating a "relatively short" time 'til his team makes its final determination.

"We're doing everything we can to make sure that this is what it appears to be," Bianco said, "and just an accident."

Sperbeck fell off of the Elway-driven cart at around 7 PM ... roughly two hours after the Hall of Fame quarterback was spotted rubbin' elbows with celebrities at a swanky day party at The Madison Club. Sperbeck sustained a significant head injury in the fall ... and was later pronounced dead on Wednesday.

Elway's attorney, Harvey Steinberg, said in a statement Friday following Bianco's statements, "This has been a terrible time for everyone involved and our hearts continue to go out to the Sperbeck family."