The sudden appearance of an alternate personality made no sense in the case of a Bay Shore man charged with killing a woman in a Bohemia motel and shooting at police three years ago, a forensic psychiatrist testified Tuesday.

That’s because Stoker Olukotun Williams, 27, now on trial before state Supreme Court Justice William Condon on charges of first-degree murder and first-degree attempted murder, had acted logically his entire life — including during and after the crime, Dr. Lawrence Siegel of upstate Valhalla testified.

People generally don’t become psychotic all of a sudden, he said.

“If someone has a mental illness, they often have a record of it before,” Siegel said during questioning by Assistant District Attorney Robert Biancavilla. But there was no sign of any mental disorder in Williams’ school records, work history or even in his interactions with police after his arrest, Siegel said.

Siegel testified on behalf of the prosecution, in rebuttal to forensic psychologist Marc Janoson, who testified Monday for the defense that Williams had a multiple personality disorder and was too mentally ill to know that what he did was wrong. Williams claimed an alternate personality named Malik committed the crime.

Williams shot Shalece Cunningham, 24, of Bay Shore in the head at the MacArthur Inn, where she used a room to work as a prostitute, on Sept. 7, 2013. He then shot at police who responded.

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Siegel noted that Williams answered detectives’ questions coherently and stopped questioning by invoking his right to an attorney — conduct not typical of a mentally disordered person.

Williams also made no mention of voices or Malik then, Siegel said. And when he later mentioned Malik, Siegel said he did it in a way that sounded fake and self-serving.

Since the arrest, Siegel said Williams has continued to act logically and with focus. For example, he did enough legal research to file a pending lawsuit against Suffolk County about his living conditions in the jail.

Siegel said he was suspicious ofWilliams’ claim that an alternate personality named Malik was responsible for the killing.. An interview and a test designed to detect malingering confirmed it, he said.

“Sometimes, unfortunately, they [defendants claiming psychiatric symptoms] don’t tell the truth,” Siegel said.