There are at least two answers to your question based upon your time period.
Civil authorities began registering births, marriages, and deaths in 1809 in many areas (1820 in Sicilia). By 1866 civil registration became law. After this date, virtually all individuals who lived in Italy were recorded.
That means that for at least 60 years of the century you specify, you will be looking at church records.
Once civil registration was in place, original records were retained by the registrar of the district.
A copy of each record is sent to the procura della repubblica—which is similar to a district court in the United States—in the provincial capital. Because the civil records are legal documents and needed for government purposes, such as military draft, the duplicate is held by the tribunale (district court).
You may need to use maps, gazetteers, and other geographic references to identify the place where your ancestor lived and the civil registration office that served that place. See Italy Maps and Italy Gazetteers for information on how to find civil registration offices.