Hi. Most Naturalization records will be held at the state archive office. For Victoria, you would need to contact the Melbourne Office. I am not sure what they offer now, having used this office over 10 years ago and this involved going through microfische. Perhaps search for its website.
I searched ancestry and got some info from the Vic Electoral rolls. Do you have that? There are also quite a few entries for USA. Even if you are not a member, you can do a general search.
Hope this helps.
first name and surname (maiden name)
Birth date and year of arrival in Australia.
Where they lived in Italy
They do have a on line record search go to
www.naa.gov.au/collection/recordsearch.aspx logon as a guest and put the surname of who you are looking for.
I have just checked and they do have a record of Naturalisation for a B.Scecchitano. Not all records are listed so you may need to write them a letter with as much details as possible.
If you find who you are loking for click on them and you will find a series number ,barcode and control symbol. print this out . then you can request for copies of thier file.
I have just done this and it cost me $ 25.00 for copies as it was a large file. The information was great and contained a copy of my father inlaws passport with his photo along with details of his application of Naturalization. It took a few months but was well worth it
If your Nonno was already in Australia and became naturalised before he married your nonna (Many people where married by proxy)and she arrived in Australia before 1949 it would class her as aquiring British Nationality by virtue of Marriage to him. so perhaps she had no need to be Naturalized.
It changed to Australian Citizenship in 1949 and was called British Nationality before then.
If you send me some details on them I will gladly do a search on Ancesty for you.