Besides the alleged gunman, Bartholomew Granger, 41, three other people were wounded, including the suspect's 20-year-old daughter, the Houston Chronicle reported.
Authorities said the shooting was the culmination of a long-festering family feud fueled by allegations of sexual assault of a child.
Granger allegedly left the Jefferson County courthouse and retrieved a gun from his pickup during a court recess and opened fire at relatives at 11:20 a.m. as police were engaged in a shift change, the Chronicle reported.
Granger allegedly fatally shot Minnie Ray Sebolt, 79, of Deweyville, described as an innocent bystander. Police said Sebolt died in the entrance to the courthouse, an unidentified person was hit in the hand, another unidentified person was shot in the back and Granger's daughter, Samantha Jackson, was critically wounded in a parking lot.
Police said several officers fired at Granger, who tried to drive off in a pickup truck that was quickly disabled by gunfire. He ran into a nearby office building and took several hostages. He surrendered about noon.
Granger was treated for wounds at a hospital, and then booked into the county jail on a murder charge.
Beaumont Police Chief James Singletary said Granger was "shooting at us and shooting multiple rounds and running like crazy."
"It was a classic shootout here that our guys handled very well," Singletary said. "He [Granger] had taken the stance that this was the day he was going to do some damage, and he did."