"At the very early stages of this investigation, initial indications were that they were what we consider circumstances of an officer-involved shooting", Hall told reporters.
The victim, Botham Shem Jean, was a 26-year-old black man.
The off-duty officer, who was still in uniform and not injured, called police to report the shooting.
The incident was initially handled as an officer-involved shooting, which meant police questioned the officer and took a blood sample but did not take her into custody, and she was placed on paid administrative leave pending an investigation.
On Thursday evening, September 6, a Dallas police officer was going home after her shift, when she walked into the wrong apartment and shot the man inside.
Jean grew up in St Lucia and attended Harding University in Searcy, Arkansas, where he often led campus worship services before graduating in 2016, the school said in a statement. Along with that, he said, "We still have a lot to do in this investigation". Hall said it's still unclear what happened between the officer and Jean.
A spokesperson for Harding University also paid tribute to Jean.
Authorities did not provide further details about how the altercation unfolded, but the officer eventually fired her gun and hit Jean.
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The shooting at the Southside Flats apartment complex, which is located just blocks away from police headquarters, left several other residents feeling uneasy.
In tribute's posted to social media following Jean's death, the 26-year-old was remembered as a "powerful singer", and a man who "always had a spirit of joy that flowed from him".
Jean worked at PricewaterhouseCoopers in Dallas, an global company that does assurance, tax and advisory work for companies around the world.
"Right now there are more questions than we have answers", she said.
Jean was listed on LinkedIn as a risk assurance experienced associate at PricewaterhouseCoopers.
The dead man's mother, Allie Jean, told NBC News she couldn't understand how the officer mistakenly killed her son.
"This is a awful tragedy".
Speaking to NBC News on the death of Botham Jean, mom, Allison Jean shared: "I couldn't believe it when we got that call".