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Psycho III (1986) Plus avec IMDbPro »

Norman commits all the murders in this film. The events of the previous film had already left him in an unstable state, but the main reason is likely a combination of Maureen's arrival waking up memories of Marion Crane, and then her relationship with Norman causing the "Mother" personality to erupt with rage. Since Norman was presumably trying to protect Maureen from "Mother," he took it out on people such as Duke's lover and the cheerleader.

The one death that Norman isn't responsible for happens right at the start of the film, when Maureen accidentally pushes a nun to her death from the bell-tower.

Norma Bates really was his mother all along. Emma Spool was her sister, as she had claimed to be, and was also having an affair with Norman's father. Upon Norman's birth, his father broke off the affair; Emma wasn't prepared to stand for this however, and eventually she ended up murdering Norman's father, and taking the baby Norman hostage, until the cops arrested her. She had deluded herself into believing Norman was her offspring, but that was never really the case.