After you get off the phone with Detective Durkin, take a look around. There's no obvious ghost, and there aren't a lot of places a ghost could be.
Hint 2
There is a door right here, but it's locked. When faced with a locked door in this game, your first tactic is not to go looking for a key; rather, it's time to send in the dead guy.
Hint 3
Joey, as a ghost, can float in midair and phase through locked doors and solid walls. So switch over to Joey and click on the door to send him in to look around.
This first room is a sort of lobby. Exit through the door at the right to find yourself on the second floor landing --
Hint 5
-- where you can see a ghost going up the stairs to the third floor. Joey can't follow her because as Rosa's spirit guide, he's tied to her and can't go more than a couple dozen yards from her.
Hint 6
So the next step is to get Rosa inside that locked door. I guess we do have to go find a key after all.