It should be noted that Mitsuru's claim of "sanity" switching isn't how the mechanics of a Cop actually work.

A Sane Cop gets 100% accurate results. An Insane Cop gets opposite results of what they should be. Paranoid Cops always get non-town investigation results. Naive Cops always get non-mafia investigation results.

In the cases of being an Insane, Paranoid or Naive Cop you are usually not told that you are Insane, Paranoid, or Naive. You are meant to deduce that on your own.

She's likely just trying to bait out the real cop and doctor. No need to give her any more information.