In the document obtained by TMZ ... Richard's manner of death is not listed -- instead, it notes the manner of death is still pending an investigation. This explains why there is still no cause of death to report.

However, it appears the fitness guru -- who is actually referred to as a "Health Motivator" on the cert -- has already been laid to rest a week after his death. Per the doc, Richard was buried here in L.A. at the Pierce Brothers Westwood Village Memorial Park and Mortuary.

The death certificate also gives some insight into Richard's private life ... which is kind of interesting as the TV personality was quite reclusive in the final years of his life. Specifically, it notes Richard was a bachelor at the time of his passing and was never married.

Remember, Richard never publicly addressed his sexuality, though many looked to him as a queer icon.

TMZ broke the story ... Richard was discovered unresponsive in his Los Angeles home by his housekeeper on Saturday morning -- a day after his 76th birthday. First responders were called to the scene, but he was sadly pronounced dead.

Though cops are investigating Richard's passing, law enforcement sources have told us they believe it's a natural death.

As TMZ previously reported ... Richard had a fall in his bathroom the night before his death after feeling dizzy earlier on. Though his housekeeper encouraged him to see a doctor, we're told he refused ... as he was celebrating his birthday.