The Navarro County sheriff's office said Thompson's wife had asked for a welfare check at the home in Frost, a city of about 600 people located about 50 miles south of Dallas.
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She told deputies she'd gone to another location with her children the night before after having a disagreement with her husband, the sheriff's office said. When she turned to the home, she thought she heard a single gunshot, left and called the sheriff's office.
A Texas man killed his two daughters before killing himself on Thursday.
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Upon arrival, deputies learned that Thompson was armed with a handgun and had threatened violence toward the family and police if anyone tried to take his children, the sheriff's office said.
Deputies also spoke with Thompson's mother, who had been in the home and spoke with Thompson and the children. Within minutes of her leaving the home, deputies heard two gunshots, the sheriff's office said.
The sheriff's office said that a SWAT team was called, and when attempts to contact anyone inside the home failed, the team made entry and found the bodies.