The shooting happened Sunday at about 12:44 a.m. at a Chase bank on Woodridge in the Gulfgate area. Investigators said an officer working an extra job nearby heard a gunshot and found the victim, a 49-year-old woman, on the ground as the man ran away.
Police believe the woman, identified as Mary Jane Gonzales, may have been shot in the head during a robbery.
So far, no arrests have been made in the shooting and police are working on getting surveillance video.
Officers are also urging people to never go to a bank at night alone.