Fortunately, these places are staffed by knowledgeable people who do an excellent job of searching the records. They have experience in dealing with people seeking older documents, and are an excellent resource.
1. The USCIS in Washington D.C. (http://www.uscis.gov/portal/site/uscis). This Office can provide a Certificate of Naturalization or a certification of nonexistence of a specific record. USCIS can be considered the best option when it comes to locating naturalization records because they contain the so-called "C-File" which is the actual certificate of naturalization that your ancestor was issued upon becoming a citizen. Most consulates require this record rather than the records below, which sometimes come from secondary sources. If your ancestor did not naturalize, consulates require a Certificate of Non-Existence of a Record from USCIS, plus census records, etc. (options vary by consulate). Currently, USCIS is running with a backlog of 12-16 months, so be sure to request your certificate from them ASAP.
2. The County Clerk's office of the county in which your ancestor may have naturalized. It can also provide the Certificate of Naturalization if the county clerk has it in their records/archives.
3. The USCIS Genealogy Program in Washington, DC (www.uscis.gov/genealogy). This office can send you a copy of your ancestor’s certificate or alien registration card, which must be supported by a County or NARA record, because USCIS will only release a certified copy to the person who received citizenship.
4. The National Archives in Washington, DC (www.nara.gov). This office collects documents from all over the United States: you could obtain a certified copy of your ancestor’s "declaration of intention," “petition for naturalization” and “oath of allegiance” from the National Archives. Documents from NARA must be certified copies, bearing the red ribbon and gold seal of NARA. If no record is found, they should issue a letter stating this. A letter from NARA stating no record is found should usually suffice for an in Italy application, as does the NARA packet in lieu of the USCIS C-File. This is good because NARA responds quickly (much quicker than USCIS) and can usually provide records in about a month's time.
5. The Regional Office of the National Archives. This office keeps Federal documents related to the States in their area of jurisdiction. You can also obtain a certified copy of your ancestor’s "declaration of intention," “petition for naturalization” and “oath of allegiance”. Documents from NARA must be certified copies, bearing the red ribbon and gold seal of NARA. If the Research shows NO RECORD, NARA can issue the alien registration card.
6. Census record. It may provide additional information relevant to your case even if based on the information provided by the individual: Immigration Records, Naturalization Records, Ship Passenger Lists, Military records, the U.S. Passport applications, Voter List Records and others (www.census.org). Ask for the first U.S. Census dated after the birth of the Italian-born ascendant’s child.
Please note that if applying in Italy, all of your American documents must be apostilled. If applying at a consulate, please follow its rules as rules vary by consulate.