The two suspects got into a car and drove off with police chasing them through several cities. Once in Kearns, the suspect fired several shots at a police car.
The suspects have been identified as Ramon S. Franco, 31, and Celene J. Hernandez, 19, both of West Valley City.
The chase ended in Taylorsville near the Salt Lake Community College after the police deployed spikes. A shootout took place, ending with both suspects wounded.
Police say Franco is in extremely critical condition and Hernandez shot herself and ran. She was found hiding on the campus of the college and taken to the hospital. It is not clear if she shot herself intentionally or not.
Two police officers are now on administrative leave pending the investigation.
No officers were hurt in the shootout.