A book existed that was supposed to be something else

This story follows a well known green haired detective. Known for solving cases in only about a week at most. He's a high skilled detective. But at times his clumsiness gets the best of him, Or of how sensitive or weak looking he is, so he gets paired up with a skilled professional trainer to solve the biggest case in the book. The immortality suicide. The greenette rolled his eyes thinking he didn't need any help. Not from another professional asshat who thought he was the shit. But he could be more then wrong.