Officers found a woman shot at an apartment complex near 41st and Garnett early Saturday morning.
Tulsa police say they received the call around 2:45 a.m.
Police believe the victim was shot at one area of the complex, ran, and then collapsed where she was found at another end of the complex.
Officers think they found the suspect nearby and gave chase, but the man was able to get away.
The victim was transported in critical, but stable condition to an area hospital.
Anybody with information regarding the shooting is asked to call Crime Stoppers at 918-596-COPS.