Rhonda Seaton, a spokeswoman with the College Station police department, told CNN that the three people killed were the constable, the man authorities say exchanged gunfire with law enforcement officers and an unidentified civilian.
In addtion, another female bystander is hospitalized at the College Station Medical Center; her condition is unknown.
Assistant Chief Scott McCollum says the gunman was shot Monday before being taken into custody.
The incident took place around 12:15 p.m. at a house in the historic district of the city close to George Bush Drive, where a gunman reportedly opened fire.
The house where the shooting took place is not far from the campus of Texas A&M University.
Texas A&M spokeswoman Sherylon Carroll told USA Today that she learned of the shooting from the campus police chief who asked her to alert students, faculty and staff to avoid the area. Within 15 minutes, police called to say the shooter was in custody, Carroll says.
"We are OK now," Carroll told the newspaper. "For a while, it was scary."
KBTX News in College Station reported that more than one law enforcement officer has been shot, and that the gunman was firing from a house with automatic weapons.