Interesting story, there is another WIP here that you could read to get inspiration : Ghost Simulator. However I think switching between Ghost and the girl is not a good idea, it could make characters overlap in personality, player hard to attach to the girl if they treat her as PC. Just a thought.
Very interesting idea. Reminds me of Beyond 2 Souls. Though playing the ghost and Katrina felt a bit disjointed at times. I think the player should be either the ghost or Katrina. Not both. That why it doesn’t feel as though the player is speaking and responding to themselves. And the relationship between the two can feel more natural.
I think instead of us picking Katrina’s abilities and thoughts she should be a set character, with you deciding things like if shes fast, smart, or mean. Other than that the ghost concept is amazingly cute, try to focus a little more on than and it will be a really amazing story.