Bob Saget Found Lying with Hand on Chest, Family Called to Check on Him

Bob Saget's family was desperately trying to get a hold of him, not knowing he'd died in his hotel room -- and cops are now painting a more complete picture of what they found there.

An Orange County Sheriff's Deputy noted in his official report that Bob was discovered by a Ritz-Carlton Hotel security staffer who'd been sent to the room on the Saget family's request ... after they'd made several unsuccessful attempts to reach him Sunday.

In the docs, obtained by TMZ, the deputy notes this staffer knocked on Bob's door multiple times before going in around 4 PM ET ... only to find all the lights off. Upon entering the bedroom, they found Bob lying face-up on the bed, with his left arm across his chest and right on the bed.

The staffer says he was cold to the touch ... and when they checked for signs of breathing or a pulse, none was detected.

Upon arriving, EMS personnel pronounced Bob dead on the scene.

Another interesting tidbit, the Ritz was able to pinpoint that Bob had last entered the room at 2:17 AM. He was scheduled to check out later that same day. He tweeted this message and photo shortly before that, at 12:42 AM, showing himself onstage in Jacksonville ... about a 2-hour drive from Orlando.

The deputy points out there were no signs of foul play or trauma. Bob's next of kin was listed as his wife, Kelly Rizzo, who was notified about his death.