The Precinct 4 Constable's Office says they chased the suspect on West Sam Houston Parkway to a wooded area in the 12800 block of Aqueduct Road near Indian Oaks Lane.
The suspect bailed out of their vehicle and disappeared in an area near the river.
Deputy constables are searching the area for the suspect, who is described only as a white male wearing a black or gray shirt.
We do not know why deputy constables initially followed the suspect.