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The incident happened in the 7600 block of Bellfort Street near Lenora just after 7 p.m.
According to Detective Ryan Cook with HPD, a woman and her daughter, who was in the backseat, were at a traffic light at Bellfort and Telephone Road.
Witnesses told HPD the suspect reportedly got upset when the woman did not immediately go when the light turned green.
That is when he allegedly fired twice inside the car and hit the young child in the thigh, police said.
Detectives told ABC13 that both drivers had cut each other off moments before the shooting.
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HPD said the suspect, who was driving a four-door black Lexus, sped off from the scene.
Cameras in the area picked up a license plate number, which police said they would use to identify the suspect, Cook said.
The young girl was taken to the hospital, where she is in stable condition, according to police.
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