Police said Robert Earl Walter, 54, is accused of shooting April Fulghum, 32, several timesat Lexington Place Apartments about 11:30 a.m.
Others in the building were not harmed in the shooting.
Walter fled and was arrested about two hours later.
His second-degree murder bond is $750,000.
Walter was fired hours earlier from his job as a maintenance worker for Fairfield Property Management, the company that oversees maintenance at Lexington Place Apartments.