We need more directors willing to take risks with films like Get Out.
He comes to the girl's apartment some afternoons to play killing games, posing her as a variety of homicide victims and snapping her photograph. The games were probably her idea, in the beginning. She called him anonymously on the telephone for many days before he had the calls traced and visited her. He is a martinet, a sadist, a bully. She is a masochist, but with her it's a game and she probably didn't expect him to cut her throat.
The murder takes place on his last day as chief of homicide; he has been promoted to head the political branch, with responsibility for spying on subversives. He takes leave of his old job very carefully, littering her apartment with fingerprints, footprints, dozens of clues. Then he helps his successor investigate the crime.
He has a compulsion to discover just how powerful he really is. He worships authority, especially his own, and like many authoritarian personalities, he has a secret dread of impotence. She hasn't helped any, with her taunts and teasing; that's why he killed her, because she ridiculed him and made love with the young radical student from downstairs. Now he will prove her wrong; he will prove himself so powerful that he is literally "above suspicion." Even though every clue points to him, the police will refuse to touch him. That is his fantasy.
Elio Petri's "Investigation of a Citizen Above Suspicion" tells this story with a clever mixture of psychology and suspense, burrowing into the inspector's paranoia while it rushes headlong into the investigation (something like "Z"). Gian Maria Volonte plays the inspector just as he needs to be played: strutting before inferiors, cringing before superiors, vulnerable beneath his cruelty.