Joan Rivers -- Autopsy Complete ... No Clear Cause of Death

Joan Rivers' autopsy has been done, but the Medical Examiner will need more information to determine exactly how she died ... TMZ has learned.

The Medical Examiner's Office tells us they've completed the physical examination of Joan's body, but could not find a clear "cause and manner of death" ... pending further studies.

We're told those further studies will include conducting toxicology testing, and interviewing medical professionals who were present during the throat procedure Joan was getting last week when she stopped breathing.

11:30 AM PT -- Melissa Rivers was just seen leaving a funeral home in NYC.