Convicted felon and accused murderer Anthony Lorenzi, 34, sits in a California lockup after he was finally arrested in connection with last month's brazen slaying.
"We will go to great lengths to bring you to justice for these victims and their families," Brown said Saturday.
Yasmin Perez, 25, and the father of her children, Gyovanni Arzuaga, 24, were both gunned down during Chicago's Puerto Rican festivities in the Humboldt Park neighborhood.
Lorenzi has been charged with first-degree murder for the shooting death of Arzuaga, but not Perez. Authorities revealed Saturday that it now appears Perez was unintentionally shot to death by her boyfriend during the frenzy that night.
"It's more than likely the deceased individual that got executed did because they were in the front seat and they were the ones getting punched and kicked and pulled. So more than likely," said Brendan Deenihan, chief of detectives with the Chicago Police Department.
The handgun believed to have been used in Perez's shooting death was found under Arzuaga's body, police said.
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Investigators said they still have no motive for the June 19 crime, which happened as Arzuaga and Perez, who lived together with their two young children in suburban Hanover Park, headed home from the festivities.
They were attacked in the 3200 block of West Division by a group of men following a minor traffic accident.
A video of the attack was posted on social media.
"It happened extremely quickly. A minor traffic accident and there's an immediate punching and kicking and pulling, and trying to harm these people inside the vehicle," Deenihan said. "Then this execution-style shots are fired into this individual's head."
Lorenzi allegedly shot Arzuaga several times, including once in the head.
"This individual in custody, Lorenzi, he is the one responsible for this death. He shoots the individual in the head several times while he is on his knees. There are others that swarmed the car and kicking and punching," Deenihan said.
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Video shows the couple lying in the street next to their car as the attackers ran off.
Arzuaga died of his injuries that night. Perez died of her injures a few days later on June 22.
The suspect is now awaiting extraction back to Illinois after being picked up Friday in the parking lot of an apartment complex in San Diego, California, Brown announced Saturday during a press conference. He's charged with first-degree murder.
"The community really stepped up and gave us several tips on who he was and that is why we were able to id him to quickly," Deenihan said.
Authorities said Lorenzi is a career criminal who has been arrested nearly 30 times and convicted of seven violent crimes. Before the fatal shooting, he was most recently in trouble for a botched carjacking, according to police.
Police said tips and security video lead to his apprehension.
"There is nowhere to run. There's nowhere to hide. We will find you and bring you to justice," Brown said.
Chicago police still have other people of interest in the crime, according to officials.