The incident was discovered just before 3 p.m. at the Michner Court Apartments on the 9400 block of E. Roosevelt Boulevard.
Police said a man in his 50s and his girlfriend, a woman in her 40s, were both shot once in the head.
Neighbors later identified the man as Mark Ruff, a U.S. Army veteran.
Police said they may have been in the apartment for days. No weapon was discovered at the scene.
The discovery was made after Reggie Mallard, a neighbor and friend, became concerned he had not seen the couple for a few days.
"The mail started piling up on his door, and that's very concerning because he's up in the morning getting his mail," said Mallard.
Mallard also noticed that he could hear that the TV was on in the apartment and so were the lights.
"Knocked on his door, no answer, no answer; I'm like 'that ain't Mark,'" Mallard added.
Mallard also said the victim's car was outside and had not moved all week.
"I got Chuck the maintenance man and, I said, 'Yo man, I ain't seen Mark in like five days," said Mallard.
A short time later, the maintenance man arrived to investigate.
Again, there was no answer.
But Mallard said when Chuck went to unlock the door, it was unlocked.
Mallard said he related to Ruff because, like him, he is also a military veteran.
"Mark was a person that was always involved with the community that's here. Whatever it is you may need, he's a person that's a giving person," Mallard added.
Police are looking for witnesses who may have seen something suspicious within the last four or five days at the apartment building.