Investigators told ABC13 the shooting happened around 4:40 p.m. at the Cleme Manor Apartments on Coke Street.
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Family members loaded the boy into a vehicle to transport him to the hospital after the shooting. EMS arrived as they were placing him in the vehicle and transported him instead.
Several neighborhood children witnessed the boy being carried through the complex to the car.
"I don't feel like any kid that young should be exposed to stuff like that because it's really bad for their mental health," Cleme Manor resident Dream Thomas said.
Investigators do not know who the gun belongs to. They interviewed those who were inside the apartment.
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This year, Texas had the greatest number of unintentional shootings in the United States. There have been 26 to date - 8 of them happening in the Greater Houston area, according to data from Everytown for Gun Safety.
"I feel like it has a lot to do with the gun laws. I feel like the gun laws here in Texas are really unfair. I feel like Texas cares more about guns than children," Thomas said.
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