To retrieve the vital records certificates of your ancestors, you should contact the Italian Municipality (Comune) in which they were born or lived. If they came from a small suburb (frazione), you should contact the Municipality of which it is part.
Italian Municipalities keep birth, marriage, and death records in their archives. It is also possible to obtain copies of a document describing the composition of the family, the so called “certificato di stato di famiglia” issued since 1869. This kind of document can be obtained from the “Ufficio Anagrafe” of the Municipalities. They contain the names, the place, and the date of birth of the family members who were alive at the time of their issuance.
Other sources of information are: a) the Italian State Archives; b) Parish Registries (Registri Parrocchiali) where, prior to the unification of Italy in 1861, certificates of baptism, confirmation, marriage, and death were filed. Many of these Registries have been subsequently transferred to the local Dioceses or the Archives of the closest major City.