The attack occurred on Saturday night at the University Heights complex, home to many students from the nearby Auburn University.
Police have not given further details, but are expected to release a statement later. They are said to be looking for a gunman.
Several emergency vehicles were seen attending the scene.
Auburn police chief Tommy Dawson told an Alabama newspaper that officers had been called to the scene on Saturday night.
He had no comment on the number of dead or wounded, or whether anyone was in custody over the incident.
Local television station WTVM is reporting that three people have died and two others were seriously injured in the attack.
The shooting happened directly in front of the complex’s main office, according to local newspaper the Birmingham News.
Auburn is the largest city in eastern Alabama with more than 50,000 people. Some 25,000 students attend Auburn University.
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