Deputies first responded to the complex, on the 2500 block of Pasadena Avenue near the Interstate 10 service road in Metairie, around 3:30 a.m., WWL reported.
Jefferson Parish Sheriff's Office spokesman Col. John Fortunato told The Advocate that a woman called 911 early Wednesday and told emergency dispatchers that she had been shot in the head.
Paramedics took her to University Medical Center in New Orleans and searched the ground-floor apartment.
Deputies found three people who died of apparent gunshot wounds when they searched the ground-floor apartment, the Times Picayune reported. Two of the victims, both men, were found in a kitchen while the third, a woman, was found on a sofa, according to The Advocate.
Their identities were not immediately released, but they all appeared to be over 30 years old, WWL reported.
Authorities canvassing the complex around 9 a.m. noticed that the door of another apartment was open and got a search warrant to go inside, according to the news station. Inside, they found a man who had been killed. He appeared to be in his 50s, although officials did not immediately identify him, the Times Picayune reported.
Jefferson Parish Sheriff Newell Normand told WWL that authorities are investigating to determine whether the cases are related.
Investigators did not immediately identify any suspects or possible motives in the attacks. Authorities continue to investigate.