The incident occurred Sunday night in Pittsburgh's Stanton Heights neighborhood, the Pittsburgh Tribune reported.
The girl, identified as Shamera Harris, 12, was getting out of her father's Ford Explorer so her parents could take a picture of her and a boy on their first date. However, the SUV started to roll backward, ran over Shamera and dragged her until it struck a tree and stopped, police said.
Shamera was pronounced dead at the scene.
Carla Harris, Shamera's mother, said her husband, Richard Benton, 53, was in the vehicle, "messing around with the gear shifter," before getting out of the vehicle, police said said.
Police said when they arrived Benton, slurred his speech and smelled of alcohol, and refused to submit to field sobriety testing.
Benton was taken into custody at the scene.