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Police said the child's grandmothers got into an argument that became physical and Brown allegedly shot Hawkins in the neck.
KDFW reported that an off-duty police officer saw Brown run across the store parking lot with the gun.
According to police, Brown shot at the officer and he returned fire but no one was shot during the exchange.
Hawkins went to a local hospital with non life-threatening injuries.
Brown was arrested and charged with aggravated assault on a public servant.
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