Cpl. Wuthipong "Tank" Tantaksinanukij say police and Emergency Medical Services on Thursday evening had responded to a domestic disturbance call near a shopping center, where they found the woman with minor injuries.
He says as paramedics placed the woman, who was on a stretcher, into the ambulance, a car accelerated toward them.
Tantaksinanukij says, "They tried to get her out of the way, but the vehicle hit her and she died around 7:45 p.m."
The Austin American-Statesman reports that no one else was injured.
Police say the man hit a marked police car as he tried to drive away and was arrested nearby.