The shooting occurred at around 3 a.m. in the 800 block of St. Marys Street, spokesman Lt. Isaac Benabou said.
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The 40-year-old male suspect is alert and stable at a hospital. Benabou said the person's injuries are not considered life-threatening.
Officers involved in the shooting were not injured.
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Benabou said police are not releasing information on how the shooting occurred until they investigate more.
The Bay City News contributed to this report.