The shooting was reported at the Sumner Houses around 8 p.m.
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The 63-year-old victim was discovered unconscious and taken to the hospital where she was pronounced dead.
The 43-year-old suspect was taken into custody and charges against him are pending.
Police say a weapon was recovered at the scene.
The victim's identity has not yet been released.
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Few other details were released, but the investigation is ongoing.
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