The incident occurred at 4 p.m. in southwest Houston, KTRK reported.
Police said an adult allowed the girl to drive an SUV, KHOU reported. The teen accidentally put too much pressure on the gas and hit the 40-year-old man and his pet, according to KPRC.
"Apparently, she pulled out and made a mistake and hit the gas instead of the brake and struck the gentleman that was walking his dog," Houston police Lt. Thurston Roberson told the television station.
The man died at the scene, and the dog died later in the day, KPRC reported.
Police did not say why the girl was behind the wheel of the car, according to KTRK. Witnesses told the television station police were giving the girl a field sobriety test,
"They did her like she was drunk," one woman told KTRK. "We were wondering why they would do that test on her if she's just like a teenager, she's not supposed to be drunk or anything."
"That's the big question," a neighbor told KTRK. "I mean, for me, I would never allow my children behind the wheel of the car, especially not at that age. Very tragic for the gentleman and his dog to be hit and killed."
Houston police said an investigation was ongoing, the television station reported.
A Harris County prosecutor said the man who allowed the girl to drive the SUV will be charged with criminally negligent homicide and child endangerment, KHOU reported.
"That's sad, that's very sad. Especially if it's a 13-year-old. She shouldn't have been driving," neighbor Julie Armstrong told KPRC. "The adult should be responsible for letting a child drive because she shouldn't have been driving at all."
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