Joe Baeza of the city police department said the 10-year-old boy and 12-year-old girl were in critical condition in a San Antonio hospital, the Los Angeles Times reported.
Baeza said the 38-year-old woman, who moved to Texas from Ohio about nine months ago, showed up at the state welfare office Monday evening, pulled a gun on two workers and demanded to see a supervisor. A supervisor arrived and talked her into letting the other two employees go and about two dozen other people in the building got out, as well, he said.
About 7:45 p.m., after talking with police negotiators for about 2 hours, the woman released the supervisor. Intermittent phone conversations with police ended with police hearing three shots about 11:45 p.m., the Times said.
The Zanesville Times Recorder in Ohio reported Baeza said those shot were Rachelle Grimmer, formerly of Crooksville, Ohio, and her two children, Timothy, 10, and Ramie, 12.
The newspaper said a spokeswoman for the Texas Health and Human Services Department said Grimmer had first applied for food stamps July 7.
"We scheduled an interview by phone with her, but couldn't reach her after repeated attempts," Stephanie Goodman said.
Grimmer's case was closed Aug. 8, she said.
"We try to give someone as much time as we can," Goodman said. "But then we heard from her again in mid-November. She knew her case had been closed and she asked that we reopen it. We sent it back for review."
Goodman said Grimmer again couldn't be reached and her case was closed for the second time Dec. 1.
"We believe we handled the situation the best we could, but it's no comfort," Goodman said. "We'll be spending a lot of time looking at this incident and seeing if we could have done anything differently. Right now, we're taking care of our staff."
Notable deaths of 2014 [PHOTOS]