A Harris County Precinct 7 deputy constable tried to pull over the driver, but he refused to stop.
A short chase ensued through Midtown, and then officials said the suspect tried to cross over the METRO light rail tracks at McGowen.
Authorities said the suspect struck another vehicle and was pinned between it and the METRO pedestrian poles.
Emergency responders pulled the man from his vehicle and transported him to Ben Taub General Hospital with a few broken bones, officials said.
The driver of the other vehicle was taken to St. Joseph Medical Center with minor injuries.
The METRO pedestrian poles were lying across the track, blocking train traffic. Main at McGowen was shut down briefly while officials picked up the poles and cleaned up some clean oil that spilled in the roadway in the accident.
Pct. 7 is investigating the incident. Charges against the suspect are pending.