FORT WORTH — A man who fled the Tarrant County courthouse Tuesday morning to apparently avoid arrest on a felony warrant led a Fort Worth police officer on a foot chase before stealing her patrol car and smashing into another motorist.The suspect and female driver of the Toyota SUV that he broadsided were both taken to a local hospital with injuries described by police as non-life-threatening.Terry Grisham, a spokesman with the Tarrant County Sheriffs Office, said the suspect was one of two men who showed up Tuesday morning at a Magistrates courtroom, located in the basement of the Tim Curry Criminal Justice Center at 401 W. Belknap St.Grisham said deputies had told one of the men that it appeared he was wanted on a felony probable cause warrant out of Fort Worth, when that man insisted that it was his friend that was wanted.Grisham said the two men were told to wait there while the deputies attempted to confirm their identities."At that point, one of them takes off through the courtroom doors," Grisham said.Grisham said deputies chased the man up a flight of stairs and outside the courthouse, requesting assistance from Fort Worth police.Officer Sharron Neal, a Fort Worth police spokeswoman, said a patrol officer spotted the suspect at West 6th and Jones streets shortly before 9:30 a.m., got out of her patrol car and took off after the suspect on foot. Neal said the suspect had led the officer through the police department's central division parking lot when he suddenly did a "180-degree turn on her back toward her patrol car" and jumped into the driver's seat."She was right behind and, at that point, she went hands on and attempted to grab him and pull him out,:" said Sgt. Pedro Criado, another police spokesman. "He resisted and pushed her off."Neal said the man sped off in the patrol car, traveling one block west on West 6th Street before turning southbound on Calhoun. She said a bike officer was pursuing the stolen patrol car and officers in patrol cars were on their way when the suspect ran a red light and broadsided a Toyota FJ Cruiser, traveling east on West 7th Street.The patrol car took out a traffic signal light before smashing into a metal fence surrounding a parking lot on the intersection's southeast corner. The Toyota also hit the fence.Kristin Hite, an XTO Energy employee working in a nearby building, heard the wreck and looked outside to see the suspect lying motionless on the street."Sitting upstairs on the fifth floor, I see a lot of accidents on this intersection and the next one so I just thought it was another accident," she said. "... Police officers were running all the way down the street and they were all standing right over him. I really thought the guy had died because he didnt move at all for a long time."Criado said in addition to the felony warrant, the suspect now also faces other felony charges, including evading arrest.He said the department will also conduct an internal review of the incident to determine if policies and procedures were followed in the pursuit of the man."Once the investigation is completed, it will be reviewed by the chain of command," he said. "The important thing here is that everyone is safe."Grisham said had the suspect stayed in the courtroom as instructed, the judge would have simply read him the warrant issued against him and set his bond. If the man could have paid the bond, he would have been free to go, Grisham said."I can't understand why a person would run out on a situation like that when he had every opportunity to walk out the same door he walked in," Grisham said. "But he chose to run out the door he came in and caused a lot of folks to run after him."