Parker County Sheriff's investigators arrested Cynthia in connection with the death of her two children, a 16-month-old boy and a 2-year-old girl.
Randolph initially told police the children, 1-year old Cavanaugh Ramirez and 2-year old Juliet Ramirez, had locked themselves in the vehicle.
The sheriff's office was alerted to the incident around 4 p.m., when temperatures outside had reached 96 degrees.
Randolph was charged Friday with two counts of first-degree injury to a child causing serious bodily injury in Weathorford, Texas.
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She spent the next 30-40 minutes looking for the children, Randolph said, before she found them locked inside the vehicle.
A Texas mother whose two children died of heat exposure after she left them in a vehicle was arrested Friday, local authorities said.
Bond has not been set for Randolph, who is being held at Park County Jail. Authorities say that the suspect admitted to locking the toddlers inside her vehicle on objective to teach them a lesson. After searching the home, the mother found them playing in the auto.
In documents released Friday, the Parker County Sheriff's Department used Randolph's shifting statements about how her children died as probable cause to charge her.
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The pair were pronounced dead from suspected extreme heat exposure and the manner of death in each child is pending, according to the Telegram. She said about 20 to 30 minutes had passed when she realized her kids were "gone".
She said she then broke the auto window to corroborate her initial story.
It was only after her nap that Randolph found her children unresponsive inside the Honda Crosstour, police said. A sheriff's spokeswoman did not immediately return a call Saturday afternoon, and jail records do not list an attorney for Randolph. During subsequent interviews with the police and with Texas Rangers, Randolph kept changing her story.
The children were identified as 1-year old Cavanaugh Ramirez, and 2-year old Juliet Ramirez. Randolph reported the children entered the vehicle on their own and had locked themselves inside.
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