However, there are usually separate offices within the town hall that do separate things. Some small towns may combine these offices as well as the duties of a few employees. Isnello in the Palermo Province is one town that comes to mind that does have both offices combined. The Municipio of Sciacca, Agrigento Province is marked by a banner out front and has separate offices for the Stato Civile and the Anagrafe, the main town offices useful for genealogical research. There was an inner courtyard which is hidden from the street.
Rarely, are the Stato Civile and the Anagrage offices not in the same building. Most times, the offices are open to walk into during their posted office hours. The Rovetta Municipio (top picture) had electronic locks on the door and you had to speak into the speaker to gain entrance. It is always good to have made an appointment. You will get better service, if they know you are coming!