The woman' body was found Friday afternoon in the parking lot of the Platt Branch Library on Victory Boulevard, according to police.
The woman was in her 40s and died from blunt force trauma, police said.
Investigators conducted a search of the area and took one person, whose identity has not yet been released, into custody.
It's unclear what led up to the woman's death and details on the relationship between the woman and the suspect remain unknown.
The investigation is ongoing. Anyone with information is urged to contact police.