The birth of every child in Italy, legitimate or natural, must be registered. Registration must occur within 3 days following the birth if done at a hospital or medical clinic, or within 10 days if done at the Municipio (city hall). More information can be found on the Ministry of Justice website (registration information only in Italian).
The birth is normally registered at the hospital or clinic by the staff. However, the birth can be registered at the Municipio by:
You can obtain the birth certificate extract at the city hall in the city or town where the birth was registered. You must specify the date of birth, name of the child, and the names of the father and mother at the time the child was born.
For further information please consult the section "Eventi della Vita - Avere un Figlio" at Il Portale Nazionale del Cittadino (only in Italian)