Antonio Alvarez, 31, and his 31-year-old wife, Amanda Alvarez, were identified by officials after being found in the vehicle in the city’s East Side neighborhood. NBC News reported that the car was not issued by the police force.
The circumstances of the shooting are under investigation but relatives of Ms Alvarez, who worked as a school teacher, say she was estranged from her husband.
A passerby discovered the victims, who both had gunshot wounds to their heads, on Monday afternoon.
They were both pronounced dead at the scene and police say that a weapon was recovered.
Trooper Alvarez was a three-year veteran of the Illinois State Police, officials said.
The family of Amanda Alvarez told ABC7 that the couple had marital issues and she had told relatives that she planned to leave her husband.
“It’s shocking and sad. This is a nice neighborhood and everybody is friendly, and it’s a tragedy,” East Side resident, Delores Williams told the news station.
Chicago Police Department says that no-one else is being sought in connection with the deaths.
“We don’t know all the details, but it’s a loss. A loss of a son, a daughter, a mother, a father- it’s a loss. It’s a big loss,” added fellow East Side resident, Carmen Flores.