The Montgomery County Sheriff's Office arrested 28-year-old Ryan Reding, of Baytown, on Thursday.
Court documents say Reding grabbed the girl by her upper arm and threatened to rape her at a Walmart in Spring in October.
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Deputies say the girl hit Reding in the arm and was able to break away.
In August, Reding was accused of traveling to two Walmart stores and separately groping two girls, ages 11 and 16 years old.
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Investigators said he first entered a Walmart store on Sawdust Road in Spring and groped the first girl. An hour later, he was spotted at the Walmart on Woodlands Parkway, where he allegedly groped another girl.
They said in both incidents, Reding headed to the back-to-school section.
He is currently out on bail.
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Man accused of groping girls at Walmart wanted