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A boy was also pulled from the pool and taken to a local hospital, the spokesman said. His condition was not known.
The Lake County Coroner's office in Indiana identified the man as 61-year-old Reginald Holiday, who was a resident of the complex.
The incident happened about 2 p.m. in the 3200 block of North Manor Drive in the south suburb, the spokesman said.
Jake Defelice, a resident of the complex, said the boy, whose age he estimated as between 8 and 12, was in the pool but could not swim and was struggling. Holiday, who Defelice said was a relative of the boy, went in to help the boy, but he too could not swim.