Monday's incident happened at about 12:40 a.m. at the intersection of North Sam Houston Parkway and Greenspoint Drive on the service road, the Houston Police Department said.
Investigators said the 53-year-old woman was in the crosswalk when the driver of a white Cadillac hit her, and she died at the scene. HPD said the 22-year-old driver returned to the scene on foot after allegedly parking near where the incident had happened.
Sgt. David Rose with HPD said the driver told them he had the green light when he hit the woman.
"At the time of impact, we don't have any witnesses that saw the light. The driver claims that his light was green, and at this point we just don't know," the sergeant said. "We did get the DWI task force officers to talk to the driver -- driver is cleared of DWI."
Rose said they're familiar with the woman in a wheelchair, telling ABC13 she's homeless and has been hit by a car in the past.
"We have members of our hit-and-run division that are here investigating with the district attorney's office, but at this time, no charges are going to be filed against the driver of the vehicle," Rose said at the scene. "As I said, causation -- we're still working on. We do not know who's at fault for this crash at this time."