The shooting happened just before 11 p.m. Thursday along the 600 block of North Olden Avenue, not far from St. Joseph's Church.
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Officials say they were called to the home for a man who was suicidal.
When four officers arrived at the scene, they encountered 22-year-old Jason Williams in the doorway with gun.
During their encounter, two officers fired their weapons.
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Williams died at the hospital.
Police recovered the gun from the scene and it was determined to be a BB gun.
The investigation is ongoing.