The block of flats is a short distance from Dallas' police headquarters.
However, it was not the right apartment.
Police have not released the name or race of the officer, who arrived home in uniform and was not injured.
Police are still determining what interaction took place between the female officer and Mr Jean. Jean was transported to an area hospital, where he died from his injuries.
Several photos purportedly of her have emerged on social media, including one of her smiling alongside a tattooed white man holding up what appeared to be white Power symbols with both hands.
"I was sitting in my apartment, I heard a single gunshot followed by the commotion".
Neighbours said they can access their building with a regular key or by using a keypad code. Her initial remarks at a news conference were also posted on the Dallas police blog. "I don't know if she was exhausted, but that's pretty scary".
Hall - who didn't provide details on that situation - said police aren't handling the case under the department's usual officer-involved shooting protocol.
"At the very early stages of this investigation - initial indications were that they were what we consider circumstances of an officer-involved shooting".
Police are now seeking a warrant to arrest the officer based on its preliminary investigation, NBC News reported.
It's not clear whether the officer is in custody, though Hall said she didn't know the officer's whereabouts. She said the officer hadn't yet been questioned. The officer has not been interviewed and was not detained.
The officer has been placed on administrative leave pending the results of the investigation.
There are still a lot of questions about the events leading up to the shooting.
Jean was shot by the uniformed police officer who "fired her weapon striking the victim", according to a police report. But given what investigators now know about the case, they made a decision to pursue a manslaughter charge, she said.
"We're all deeply grieved", Jana Rucker said.
After graduating in 2016, Jean began a risk assurance internship at PricewaterhouseCoopers.
"This is a awful tragedy", the company said in a statement".
After excelling in high school, she said, her son left the island about seven years ago to study accounting and management information systems at Harding University before he was offered the job in Dallas.
Harding President Bruce McClarty remembered how he once asked Jean to lead the chapel in a hymn that Jean had never heard before, according to reporting from the Christian Chronicle.