Officers responded to reports of shots fired at the intersection of North Main Street and Olive Avenue just before 2 p.m. on Sunday.
Livingston Police Interim Chief John Ramirez confirmed Monday that the man and woman knew each other and had a child together.
Ramirez also said the woman died at the scene.
Investigators are still working with dozens of witnesses to determine what happened.
Action News spoke with witnesses and residents at the apartment complex where the shooting happened.
One woman said she heard the shots just outside her window, as she was sleeping with her toddler and newborn baby, only two days after giving birth.
"Then I heard it again. I heard it like two, three times, maybe the shots again. And that's when I got even more scared and made sure, like, the windows were closed. Because, I mean, it was just me and my babies here," said the woman, who asked to remain anonymous.
After the initial shock, neighbors quickly realized they weren't in danger: witnesses say the shooter then turned the gun on himself.
"I heard my neighbors shout, 'he shot himself, he shot himself!" said the woman Action News spoke to.
Once police arrived on the scene, witnesses say they learned a little boy who was near the man and woman was their son.
"Words can't really explain it. It's very hard for a little boy to see... watch everything in his own eyes," said another resident who also asked to remain anonymous.
The man's family spoke to Action News on Monday, asking the community not to jump to conclusions.
"Just don't judge him for what's going on online. No one knows what really happened," said the man's brother, Victor Panleon.
The man's wife, who asked that her name not be shared publicly, said this is a difficult time for her own children. And in the midst of it all, concern too for that little boy who witnessed the shooting, his mother now dead.
"Right now, the baby boy... where is he? I don't know if he has eaten; he's a very picky eater. I don't know if they're gonna give him the food that he likes. Or if they're gonna put his favorite cartoons," said the man's wife.
Neither the police nor the man's family has identified either of those involved in Sunday's shooting. His wife says he is in the hospital in critical but stable condition.
This is an ongoing investigation.