That sounds like a standard point-and-click system. The main system of the game would rely on reacting to touch/click events, touching certain images or invisible hitboxes would trigger an action, be it a text dialog, move to another screen, etc. (Example: Touch --> Is Touching --> Torn Paper)
You'll also want to heavily rely on lots of global variables, to tell if you've already picked up evidence or talked to someone, because you'll want different things to appear (or disappear) depending on how much you've progressed in the game.
After you build that system, you'll find it easy to place all the different sprites together at the right times!