The reports that Michael Jackson spent the last night in his bedroom are not true -- we've learned Jackson spent his last hours in Dr. Conrad Murray's bedroom ... in Dr. Murray's bed.

Multiple law enforcement sources tell us Jackson did not want people going in and out of his room, so he used Dr. Murray's bedroom for his IV Propofol. We're told Dr. Murray administered the Propofol to Jackson hours before he died, while the singer lay in Murray's bed.

Law enforcement believes Dr. Murray may have been using his room almost nightly to administer Propofol to Jackson. Emergency workers found an IV stand, an empty IV bag and oxygen tanks in Dr. Murray's room. And as we first reported, the Monday after Jackson died, cops found a stash of Propofol and other drugs hidden in a closet connected to Dr. Murray's room.

We've already reported Dr. Murray left the room at some point when Jackson was receiving an IV drip of Propofol and may have fallen asleep. Cops believe by the time he awakened Jackson's heart may have already stopped beating.

We're told Dr. Murray was not in Jackson's house during the day. He would show up in the evening and leave in the morning. Law enforcement believes the doctor may have regularly gone to Jackson's home at night to administer Propofol so the singer could sleep.

Law enforcement believes Dr. Murray could have discovered Jackson sometime around 9 AM the day of his death. One theory cops are working under ... after discovering Jackson either in distress or dead, Dr. Murray called two employees at his medical office in Houston and told them to go to his storage unit and remove certain boxes. Both women told TMZ Dr. Murray did not call them but cops are dubious. The stories of the two women conflict -- one says a box of dirty needles was retrieved; the other says she went to retrieve a chair.

As for what may have been in the boxes, law enforcement is investigating whether Dr. Murray had Propofol delivered to his Houston medical office ... possibly put in his storage unit ... and then FedEx'd to Los Angeles as needed.

Dr. Murray rented the storage unit April 1 and the staff went back on 4 different occasions before Jackson's death.

We know when the DEA raided Dr. Murray's Houston medical office, they seized a rolodex card with FedEx information.