I like the concept and the art design, but the limited amount of times you can question anyone is what hampers this game. Since when is a detective only allowed to question 2 out of several witnesses and suspects? Once you use them up, then you're basically left with vague clues and have to resort to guessing. Even worse, after I completed the first case, my next case had almost a dozen people to question, and only one AP to question a single person!
I'd recommend either giving the player more AP from the start, or just doing away with them in the first place and let the challenge of the game come from using logic and reason to sort out the clues and find the culprit.