Houston police spokesman John Cannon said Bellaire police Cpl. Jimmie Norman, 53, and another man, possibly the body shop's manager, were fatally wounded about 8:50 a.m. outside the Maaco shop, The Houston Chronicle reported.
The gunman, also unidentified, was critically wounded, the newspaper said.
Cannon said Norman had pulled over a car for a traffic violation, but the driver sped away. The officer gave chase and the suspect hit a pickup truck before pulling in to the body shop's driveway. Norman and the suspect got into a confrontation and the suspect drew a handgun and shot the officer, Cannon said.
"He didn't get an opportunity to draw his weapon and defend himself," Cannon said.
The gunman then fatally wounded a man who walked out of the auto body shop, Cannon said.
"He pretty much at close, blank range murdered a Bellaire police officer and an innocent bystander," Cannon said.
The gunman then shot at two other Bellaire police officers who showed up. They returned fire and wounded the man, who fled. They found him nearby trying to hide under a truck and he was taken into custody and hospitalized in critical condition.
The pickup driver was not hurt.
Cannon said it was unclear why the gunman opened fire.
"There are a lot of 'whys' in this," he said.