Bastrop Police Det. Vicky Steffanic said at a news briefing on Saturday evening that the dead were one man, two women and a child.
Another child was taken to a hospital with injuries that were not life threatening, she said.
“The shooter is among the dead and there is no further threat to the public,” Steffanic said.
The identities of the dead are not being released pending notification of family.
Steffanic declined to comment on a motive for the shooting, the Toronto Star reported.
At least one nearby resident told the Austin American-Statesman that those found dead were residents of the complex.
Police initially said there could be as many as five dead, but that was later revised to four when it was determined that the suspected shooter was among the fatalities.
Bastrop is a town of about 7,500 people located about 55 kilometres southeast of Austin.