Mystery is all about puzzle. Deeper characters provide more puzzling challenges to your sleuth. Your sleuth is challenged by the obstacles the other characters throw his way. One of the best ways to create a puzzle for your sleuth is to give each character a secret and a lie.
Or more than one.
Secrets and the lies characters use to preserve the secret add a human dimension to characters.
Whether it’s the villain or a suspect each character has things they don’t want others to know.
Your sleuth is challenged by diving through the lies to get to the truth that lies underneath.
Ultimately, he must separate the various truths to get to the one that reveals the killer.