The documents you will need will be different for if you are from another EU country or from outside Europe. Bearing Brexit in mind, you may find your comune will have even less idea than usual as to what they require.
Best advice is to go and ask them ASAP, before it all changes.
Basic documents will be passport, codice fiscale, proof of house ownership, bank balance and health card. But each comune does things differently.
Also bear in mind that once resident you are required to make yearly tax returns in Italy.