Former Minneapolis police officer Mohamed Noor has pleaded not guilty to the murder and manslaughter of Australian life coach Justine Ruszczyk Damond.

Noor is accused of shooting dead the 40-year-old Australian woman in an alley behind her Minneapolis home after she called police in 2017 to report hearing a woman’s screams.

Prosecutors charged Noor with second-degree murder, third-degree murder and manslaughter. The trial is scheduled to begin in Minneapolis on April 1.

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During a brief hearing on Friday in Minneapolis, 33-year-old Noor entered not guilty pleas to the charges and judge Kathryn Quaintance made several pre-trial rulings.

Noor refused investigators’ request for a voluntary interview, and prosecutors said they should be allowed to tell jurors that.

But Judge Quaintance rejected that on Friday. “It seems to me the right not to incriminate oneself is a pretty seminal constitutional right,” she said.

Though Judge Quaintance ruled that prosecutors can’t use Noor’s silence in their “case in chief”, she did say it might be used to impeach his testimony if he takes the stand.

Judge Quaintance also rejected prosecutors’ bid to use a 2015 psychological test of Noor before his hiring as a police officer.

The test found that Noor was disinterested in interacting with others and was more likely to be impatient or have difficulty confronting people. Still, a psychiatrist concluded that overall, Noor was fit to be a police officer.

Prosecutors had argued the test results were admissible as character evidence, and they matter because the jury has to decide whether Noor acted as a reasonable police officer would act. But the judge sided with the defence, who called the test “unsupported speculation.”

Among Judge Quaintance’s other rulings, she said prosecutors can’t point to prior “bad acts” during Noor’s time as an officer, including one incident in which prosecutors say he pointed a gun at a motorist’s head two months before Damond’s shooting.

Former Sydney-sider Ms Damond was dressed in her pyjamas just before midnight on July 15 last year at her Minneapolis home.

When she heard what she feared was a woman being raped, she called 911.

After calling police, she saw a squad car driving down the alley behind her house. As it pulled up 50m away, she approached it in the darkness.

Mohamed Noor shot from the passenger seat across his partner Officer Harrity and out the window at Ms Damond. The bullet hit her in the stomach and she died at the scene.

Noor was fired from the Minneapolis Police Department after the charges were filed last year.

Before he faces trial in April, Noor is also dealing with a civil lawsuit filed by Ms Damond’s family, alleging a cover-up.

The lawsuit claims Noor and his partner that night, Officer Matthew Harrity, conspired to cover up facts surrounding the shooting and made a conscious decision not to activate their body cameras.

“Had they done so, there would be video and audio recording of the fatal shooting of Justine, and Harrity and Noor would not be free to concoct a story in a vain attempt to insulate Noor from civil and criminal liability,” the lawsuit says.

The lawsuit, filed by Ms Damond’s father, John Ruszczyk, seeks monetary damages. It names both officers, the city, and the current and former police chief as defendants.