Six people were taken to nearby hospitals, CBS Dallas reported, adding that one person died.
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.
Dallas Fire and Rescue officials said the metal frame collapsed into the apartment block near Good Latimer and Live Oak in Downtown Dallas.
The crane crashed into the east side of the Elan City Lights residential building, where crews found a woman inside an apartment and she was later pronounced dead, Dallas Fire-Rescue spokesman Jason Evans said, according to The Dallas Morning News.
Evans said it is too early to say whether there may be more people hurt, killed or missing.
"Our hearts go out to everyone who has been impacted by this incident".
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Officials confirmed that two people were also in a critical condition and that three others were in a serious condition. "We only hope that the damage that's been inflicted thus far is where it stops", he told the news outlet. "And then it just got dark very quickly and the wind picked up something fierce. It went from the fifth floor to, from what I can tell, the third floor", she said.
Allen told the paper he saw a bloodied woman trapped in her apartment on the second floor.
There were also reports of hail damage to windows in Richardson and Collin County, and hail measuring about 1.5 inches was reported in Garland, National Weather Service meteorologist Joey Picca said.
When it hit the garage, she added, "We just saw cars everywhere".
He said the cause of the crane's collapse was uncertain buthe felt there was a "strong possibility" that the winds "played some role in the collapse", according to The Associated Press.