"He told them that he is a shooter and 'you're dead, and you're dead,'" school district Superintendent Donny O'Dell told the station.
Miller revealed that he was conducting his own active-shooter drill as students were arriving at 8 a.m., the Dallas Morning News reported. He said he wanted to speak to the principal.
School officials knew Miller because he has a child enrolled at the school. They waited until he left campus to alert police, who arrested him on charges of third-degree felony terroristic threats. His bail was set at $75,000.
The incident comes at a time of high tension in schools following several tragic shootings in public places, including the Sandy Hook Elementary School massacre in Newtown, Conn. on Dec. 14 that claimed the lives of 20 children and six adults.
Parents at Celina Elementary School, however, weren't so quick to demonize Miller for the alleged act. David Siano told NBC-DFW that the school needs to review its security measures.
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"We are not prepared," Siano said. "His intent was just simply to say, 'you've done nothing' and that's what it showed... So if that's what it takes, it's a shame."