It happened at about 2:45 p.m. in the 4400 block of North Freeway near East Crosstimbers.
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The driver failed to see the woman on the ground and his rear tire ran over the woman's head, according to police.
Officials with the Houston Fire Department later arrived and found the woman, who is believed to be homeless, slumped over a pool of blood.
Police said the man and his 10-year-old son remained at the scene and were cooperating in the investigation. Authorities were going to run a test to make sure the driver was not under the influence at the time of the incident.
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Lt. Jesse Dang advised people, whether driving or walking, to look around all 360 degrees in busy parking lots during the holidays.
"Make sure you're paying attention, driving or walking, to avoid these types of incidents," said Dang.