Of those injured, two were listed in critical condition, three had suffered serious injuries and one suffered minor injuries and was later discharged from a hospital, Evans said.
It wasn't immediately clear whether any other people were missing or trapped in the building or the nearby parking garage, which also collapsed.
By 4 p.m., the storm had moved south of Dallas, leaving a mess of downed trees, some street flooding and other wind damage across the metropolitan area.
A photo provided by Michael Santana shows a collapsed construction crane at the Elan City Lights apartments in Dallas after severe thunderstorms on Sunday.
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Dallas Fire and Rescue reported the incident was near 2600 Live Oak St., where the City of Dallas Office of Cultural Affairs' Latino Cultural Center is located.
"There has never been a crane collapse onto an already inhabited building, as far as I know", Evans said Sunday.
The highest recorded gust in the area was 71 miles per hour at Dallas Love Field, according to the National Weather Service, though winds were likely higher at the elevation where the crane was on top of the building.
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Two people have reportedly been rescued and hospitalized.
Most of the crane collapses that have been dealt with, Evans said, involve the crane collapsing onto itself or onto a building that's vacant or under construction. Search crews found a woman who was later pronounced dead.
The crane also fell onto the parking garage, Kearney said, so she and her husband went to go check on their vehicles.
A powerful thunderstorm toppled a crane Sunday afternoon in downtown Dallas, authorities reported.
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