Well there are some factors here...
Who saw her that morning - what was her condition that morning - what was her condition the evening before - who saw her the evening before.
Who's name was the Demerol in? (so far it sounds like it was in someones name that was not Anna's or any of Anna's aliases.)
If it was in Howard's name why was Howard injecting her with large doses of HIS Demerol?
Or....
Why was Howard leaving his drugs laying around if she was the one who injected herself with the Demerol?
Everything is pointing to Howard being the drug controller so she would not OD. Howard has been seen injecting drugs into her in the past. Then it is very possible that the Demerol was in his name.
Also if she injected the Demerol by syringe by herself then why not leave the syringe in the room sense it would have Anna's fingerprints on it. Most likely if she did it to herself while everyone was gone then the syringe would probably be by the bedside, in the bed or in the room somewhere.
Really.
(just helping her /sarc)