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Authorities said Dorian Mendoza was involved in a verbal fight with the girl's mother when he picked up the 4-month-old rabbit named "Bunny" and threw it against the wall, killing it.
Officials said the couple was fighting over the rabbit.
Reports state he had bought his daughter the rabbit a few weeks earlier.
Deputies arrested him for animal cruelty.
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He also had an unrelated active arrest warrant for possessing a sawed-off shotgun.