Three Midlothian Police Department officers and a Texas state trooper were hospitalized for treatment of their wounds, Midlothian Police Department spokesman Britton Snipes told CNN.
Police were called to the scene when a resident called to report her window had been broken. They determined it had been broken from a gunshot and went to the apartment where the gunshot seemed to have originated.
"They were immediately fired upon," Snipes said.
The suspect was identified as 25-year-old Richard Miles.
About two hours after the first shots were fired, gunfire broke out again. News footage showed police firing into the apartment were Miles was holed up.
Police said Miles shot at officers who threw a telephone into his apartment intended for use in negotiations, the Dallas Morning News reported. Police said no one was injured during the exchange.
The wounded officers were being treated at Methodist Dallas Medical Center.
Texas state trooper Rick Smith was listed in good condition, and was said to be conscious and talking, after being shot near the right eye. The bullet was lodged in his neck.
Midlothian Officer Dustin Compton, 30, was reported in good condition with a gunshot wound to the calf. Officer Cody McKinney, 28, was shot in the elbow, knee and thigh and was listed in fair condition. Sgt. Brian Woolery's injuries were not known Sunday evening, the Morning News said, but he was in the intensive-care unit and listed in stable condition.