The shooting unfolded at the Oleanders at Broadway apartment complex off 52nd Street and Broadway Avenue J.
Galveston police said they were called to the apartments for a fight happening between a 911 caller and their boyfriend around 7:30 p.m. Sunday.
The caller told police they thought the man was armed and he was still at the apartment complex.
When officers arrived at the scene, they spotted the suspect. Investigators said he ran off, but officers chased him through the parking garage and around some common areas of the complex before the shooting happened.
"He then evaded on foot. A foot chase ensued, which ended here near the area of 53rd Street and Ball Avenue, where an officer-involved shooting occurred," Lt. Jeff Banks said.
Police did not say if the suspect pointed a weapon at the officer or if the suspect fired any shots. They said that's part of the ongoing investigation, though they did note that a weapon was recovered at the scene.
The suspect was taken to the hospital after being shot, according to Galveston police. Investigators did not immediately release any information about his condition.
The officer was not hurt.
The Texas Rangers and the Galveston County District Attorney's Office are both investigating the shooting.
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