I agree with "From Chicago" that this is a General Info line, so whoever calls from the Cook County Govt may appear as calling from the 312-603-5500 line.
If you have any business with Cook County, simply call whatever office you have business with and see if that office called. I received a call from 312-603-5500 but heard nothing. I remembered that I'd requested archived files last week, so I called the General Records, Probate line. The file I requested had indeed arrived.
I just received a call too- the guy said he was a private investigator and was doing a background check on someone that applied there and my # was given as a reference. I have never heard of the person he was asking about.