Unfortunately, even with official status as investigative psychic, you haven’t learned anything so far that tells you who the murderer is.  If pressed, you'll go with Mrs. White, the most likely suspect.  However, you shouldn’t risk a definite accusation until you have no other choice. 

Keep up your contacts with the servants.  They have ways in and out of the locked rooms that no one else knows.  Anything that they tell you can be fed out as psychic “visions” or used to find additional clues.  Be sure to deliver only when asked; you don’t want a long dry spell with nothing to report.

It’s also a good idea to watch your back.  The murderer might not try to kill you with the Inspector in the same house, but if you’re getting good leads, you will represent a real threat.