You live in Chicago, or so it seems from the original post in this thread. The fact that the police take an hour or more to respond to a report of a property crime (vandalism or theft) is understandable. In fact, in many cities the police no longer respond at all to property crimes complaints, so consider yourself fortunate.
In Illinois if the police decline to file charges with the State's Attorney, you can attempt to contact the Victim Services office of the State's Attorney's Office to file an informal complaint. THAT is probably what the police were trying to tell you to do. For whatever reason, the police do not seem to feel that what they know of the matter rises to the level of a criminal act. It may well be that they think the matter is civil ... or, that the perpetrator is mentally ill and unable to be legally charged.
I also have to ask, could the issue be one of language? Is English your first language? It may be that you have had a difficult time with the police because you have not been able to adequately communicate with them what happened and who witnessed the events you believe prove that this guy did them.
Police contacted me by phone and advised to go to the court located near the intersection of W. Harrison St. and Kedzie Ave. As a police representative explained to me this court is branch #43 of local court system. Now, I found by google that this court belong to Branch 43, Misdemeanor/Ordinance:
http://www.cookcountycourt.org/ABOUTTHECOURT/MunicipalDepartment/FirstMunicipalDistrictChicago/MisdemeanorSection.aspx
The court is really located near the intersection of W. Harrison St. and Kedzie Ave in Chicago.
https://www.google.com/maps/place/3150+W+Flournoy+St,+Chicago,+IL+60612/@41.8730282,-87.7076522,17z/data=!3m1!4b1!4m5!3m4!1s0x880e329999bbd313:0xa46116d5fa6c8d01!8m2!3d41.8730282!4d-87.7054635
It seems the Chicago police want us to do its job.
A business owner lives in Chicago more than 20 years. He negotiated many successful business deals. I live in Chicago from 2002 year and graduated from Wright college and University of Illinois in Chicago.
Therefore, it seems that we have good command of English. We understand that we need more practice in English.
A mental state of the perpetrator was not yet evaluated for the purpose whether he could be tried in criminal court. I could judge from his conduct and his words that he pretty well understand what he is doing.