John Lee Cowell is accused fatally stabbing 18-year-old Wilson and injuring her sister in July at the MacArthur BART station.
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The judge heading up the trial made the decision to suspend proceedings Thursday and plans to appoint doctors to examine Cowell's mental competency.
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Cowell's attorney told the judge last week she questions his mental competence.
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If Cowell is found incompetent, the case will be put on hold while he gets treatment at a state hospital.
Nia Wilson's family was at the court hearing Thursday and expressed disbelief with the defense's argument.
"If this guy could do what he did and change his clothes and carry out what he did so smoothly, you know, I think that's pretty competent," said Ansar Mohammed, Nia Wilson's father. "I want justice for my daughters. That's the only thing I want is justice for my daughters... fair justice for my daughters."
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After that statement, a reporter asked if justice to him would be the death penalty.
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"Nah, I leave that to the creator, that's not my decision," replied Mohammed.
Because Cowell is charged with murder and the special circumstance of lying in wait, he would be eligible for the death penalty if convicted of killing Wilson.
The district attorney's office delayed their decision on seeking the death penalty after questions about Cowell's competency were raised.
For more stories and videos on the Nia Wilson case.