Detroit police homicide inspector Dwane Blackmon said one of the missing is believed to be a woman who worked at Park Medical Centers on the city's west side and the other is a man who entered the building with a gun.
"Initially, what we know is, is that it was an arson fire," Blackmon said. "It was started by an individual who we believe fired some shots prior to the fire being started.'
Antha Williams-Hill told The Associated Press that her daughter, Sharita Williams, is the missing woman. Williams-Hill said Williams worked at the office as a medical assistant.
Blackmon said he couldn't release names or provide more details of the incident.
Podiatrist Stuart Kirschenbaum said he was at his office in the building when he learned there had been a shooting. Kirschenbaum said a security guard yelled to him that a man who used to work at the building had grabbed a woman and was firing at others.
"Everyone called the police and we started running," he said. "And before you knew, it we saw fire coming from (a) clinic down the hall. Then we started seeing smoke coming from the end of the building."
Firefighters had largely brought the blaze under control by late morning.
Clinical psychologist Kim Logan Nolin also has an office at the single-story building. She said she was on her way to work about 9 a.m. when a worker already at the building called to her to say it was on fire and that there had been a shooting.
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