Irizarry filmed the video about a month ago, but it has gained recent traction and since been watched more than a million times.
The investigators are expected to interview the officer this week about the incident, adding that the investigation would wrap up soon.
"The incident ... is completely unacceptable", Preckwinkle said.
"I apologize to the young woman who had this awful experience".
The officer "should have intervened", Preckwinkle said.
Last month, Mia Irizarry was celebrating her birthday at Forest Preserves of Cook County in IL. Irizarry insisted as she backed away from him, which only made the man more irate.
Police have not released the name of the suspect nor the name of the officer. The officer was identified as Patrick Connor, a 10-year-veteran of the force who had previously been disciplined for working a part-time job and not carrying proper credentials, Forest Preserve District Police Chief Kelvin Pope said in a Tuesday news conference.
Mia Irizarry rented a pavilion at Cook County Forest Preserves in IL for an afternoon picnic on June 14.
"You should not be wearing that in the United States of America", the man tells Irizarry. "I would like to know is she an American citizen? Are you a United States citizen?"
Puerto Rico is a U.S. commonwealth, with its residents being considered USA citizens since 1917.
Iran says no major change in oil exports despite U.S. pressure
Boosting production this way might risk a decline in oilfield pressure that could result in long-term damage to the reservoirs. But now there is growing worry that even a one-million-bpd increase will not be enough.
"Period", the man insisted, ignoring Irizarry's comments that she was only there for a birthday party and was not trying to "change anything".
"Officer, I'm renting this area and he's harassing me about the shirt I'm wearing", the woman says. "In this case, a U.S. citizen questions the citizenship of another United States citizen and American law-enforcement just sits back and watches". "I do not feel comfortable with him here, is there anything you can do?"
"We have worked very hard since 2010 to make the Forest Preserves of Cook County a welcoming and safe place for all", she tweeted. Trybus resumes his abuse, saying: "You're not American, if you were American you wouldn't wear that".
"Well, I guess you just never know", replied Irizarry. She warns him that he could be arrested "for not being compliant".
The harassment continued, as Irizarry repeatedly called on the officer for help, asking, "Is there anything you can do?"
"If you're drunk, you don't belong here", she is heard telling the man.
The man's behavior towards Irizarry appears to have been witnessed by a nearby police officer, who does not appear to stop the man from continuing to verbally harass her, despite her requests for help.
"Hopefully, this officer will actually do something", Irizarry is heard saying when the second officer arrives. She purchased a permit to rent a picnic area in the park, and arrived wearing a shirt that displayed the Puerto Rican flag.