In Chicago, you can bring a deceased cat to Chicago Animal Care & Control for proper cremation without appointment during their operating hours. For pick-up, call 311. The 311 Operator will create a report that goes to Streets & Sanitation, who will recover the cat (or any other animal) and bring it to Chicago Animal Care & Control (CACC). You can also place the cat in a trash bag and let the 311 operator know where it is. CACC should automatically scan for a microchip, but we recommend making this request specifically when you talk to the 311 operator.
Outside Chicago, contact your local village office, police station or animal control facility to inquire what their procedure is.