The Houston Police Department said officers attempted to stop a suspect wanted on a felony charge for possession of a firearm when the man ran off on foot.
Lt. Larry Crowson said the officers called for K-9 units and the HPD helicopter to locate the suspect, who ran into a neighborhood in an unincorporated part of the county.
Harris County sheriff's deputies soon joined in the search.
Neighbors called 911 to report a man who was jumping over fences near the 13900 block of Beckwith near Rushworth Drive. This is not far from Ella Boulevard.
An off-duty officer fired a single shot at the suspect, but neither man was injured in the shooting.
HPD says officers eventually caught up with the suspect, who was found behind a palm tree in someone's backyard.
"A K-9 officer made contact with the suspect on the leg," Lt. Crowson said. "He's being transported to the hospital."
Police say the suspect may face upgraded charges after two weapons were found discarded during his foot chase with officers.
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