Tacoma Police Department spokesman Mark Fulghum said detectives believe the woman who was driving the vehicle ran over the victim intentionally, then left her for dead, based on information obtained during an investigation into the crash.
The victim was later identified as Michelle Johnson, 45, of Burien.
The driver has now been booked into Pierce County Jail on suspicion of first-degree murder, according to police records. She is identified in booking documents as a 33-year-old Tukwila woman with a prior arrest for theft.
According to detectives, the crash happened at the intersection of South 43rd Street and South J Street at about 8:20 p.m. Friday.
Police say the two women knew each other but got into an argument just before the crash.
Johnson was walking in the intersection when she was hit by an SUV driven by the other woman. Police say the driver suddenly made a left turn as Johnson stepped into the intersection.
The car knocked Johnson over - and she was left to die in the street.
Neighbors say the suspect took off in a hurry because they could hear tires squealing. But police say the driver called 911 a short time later, then turned herself in.
Detectives say the driver spent much of the night with Johnson, but the two women got into a fight and separated.
That's when the suspect got in her car, drove up behind the victim and waited for her to cross the street - then stepped on the gas, police say.
"I heard like a thunk, almost like a watermelon, and then a squealing of the tires," said neighbor Bob Johnson, who is no relation to the victim. "I'm pretty sure it was her when she hit the person, ran over her, and just took off."
Another neighbor, Mike Piatz, says, "I seen an ambulance giving CPR to a lady. And she was just laying there. ... And I just drove home. I thought it was maybe a heart attack or something."
Johnson died at the scene.