Go left - go pass the two patients talking by the fountain, the next one, who's standing alone at the door, and two men in white smocks. Enter the room left from them (the name of the doctor is hanging on the door). Talk to the man inside. During the test with the polygraph chose answers according to your liking (although, if you want to unlock One flew over the nut-job's nest then you can't allow your heroine to lie - options: 1, 1, 1 or 3, 1, 1 or 3). When after the test ends (achievement: One flew over the cockoo's nest) the doctor says that Kate's things are in the drawer. Approach the tall, narrow chest of drawers in the corner of the room.
In zoom, slide out the second drawer by sliding the mouse down and collect the things.
If you want you can check out the room right behind Dr. Mangoling's office (the blue metal ornate door) and speak with the two oldest patients (required for an achievement).