Novels by Henning Mankel that have as protagonist to inspector Kurt Wallander you can opine are police books. "Sidetracked" is one of the best, dealing with the theme of a psychopathic killer.
But I personally find the author uses the hook of mystery to expose a big amount of questions so important if not more that the criminal plot. We can begin with the personality of Wallander, a policeman nothing usual, too much sensible for so hard, cruel facts he think has to face, although he overcomes his personal limitations when necessary, but at a considerable personal cost, drinking enormous amounts of coffee and breaking rules and ordnances. For that, in this novel, Wallander lets subconsciously to be sidetracked to avoid the horror he suspects from the beginning. From his police station of Ystad, a small village of South Sweden, the crimes Wallander has to solve, serve an excuse to expose a background of social and politic disarrangement rounding the chaos, details very notable as Swedish society is seen from outside as calm and very equalitarian, although this cases have frequent international implications that go much more far from Sweden. Psychology, ideology, politics and sociology are in this books as relevant as crimes and action. All that it's an engineering piece not easy to ensemble, and some of his novels are better achieved than others, and suppose even can disgust to readers which don't want more than a thriller or disagree with the general thesis of the author.