"At this point there is a report that one person may have suffered a wound from the hatchet," he said, adding that the local fire department is still trying to sort out what injuries occurred.
Aaron said the police response was "swift" as an officer entered the theater where "Mad Max" was showing, and encountered the gunman who began to fire his weapon. The officer, Aaron said, returned fire and backed out of the theater.
A SWAT team responded, engaged the gunman, and the gunman died "just inside the movie theater," he added.
"We believe the imminent threat has been ended," he said., but added that police are investigating two backpacks the gunman had brought into the theater to make sure they are not hazardous in some way.
Officials are expected to detonate the backpack of the suspect, according to a police spokesman.
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Live video from the scene showed that the movie theater was cordoned off by crime-scene tape.
Nashville Fire Department spokesman Brian Haas said that police were responding to the scene, and WSMV cited a witness who said that officers had fired shots during the incident.
The report from Antioch comes about two weeks after a gunman opened fire inside a movie theater in Lafayette, Louisiana, during a screening of the film "Trainwreck." Police there said John Russell Houser killed two people and wounded nine others before fatally shooting himself.
—The Associated Press contributed to this report.