It is hard to say how long it may take to receive the document requested, as it depends on the individual comune handling the request. Average time to complete is 3-6 months, but by law they have up to 6 months to fulfill the order. Ultimately, you will either receive the record(s) requested or a notification of No Record Found.
PLEASE NOTE: After Italy passed the New Immigration Law (No. 113/2018) in 2018, processing time for Italian Town Halls to issue civil vital records (births, marriages, etc.) requested for the purpose of filing for Italian Dual Citizenship is now SIX (6) months. Although most Italian town halls fulfill these kinds of requests much faster, larger cities may take longer to respond.