Sheborah Thomas, 30, was charged with capital murder and "all indications are she is the one who acted alone" in the deaths of her 7-year-old son and 5-year-old daughter, Houston police spokesman Kese Smith told The Associated Press.
Authorities have not yet confirmed a cause of death but said the woman allegedly told an acquaintance that she had drowned the children.
Smith said investigators were still interviewing the woman and had not determined a motive. She was turned in to police by the acquaintance, who came upon her throwing away trash in a field, where she allegedly told him she needed help moving right away.
"She was so matter of fact about it he didn't think she was serious. He thought she was joking," Smith said. "He continued to help her pack."
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Smith said the man eventually realized something was wrong when he asked again and got the same answer. He then drove the woman toward a nearby police precinct and flagged down an officer, Smith said.
The mother apparently tried burying the children at first but put them under a neighbor's house when that proved too difficult, Smith said.
"She would just take her kids to the park; that's all everyone saw of them," neighbor Mike Polk told the newspaper. In 2001, Houston mother Andrea Yates drowned her five children ranging in age from 7 years to 6 months in the bathtub of her family's home. She was eventually found not guilty by reason of insanity in July 2006 and sent to a state mental hospital.