Sometimes you can narrow it down through the census. They will tell you if they were an alien, applying for citizenship or already naturalized.
Start with the census (1900 - 1940 listed citizenship) to determine when it might have become a citizen (the information is not 100% accurate, but it is a start of where to look). Then look for naturalization records from the county or state where he lived.
Dear Mr. Magliaro,
Thank you for posting your request on History Hub!
As the previous posters mentioned, the 1940 Census will note the citizenship status of your grandfather. We searched the National Archives Catalog and located the Population Schedules for the 1940 Census in the Records of the Bureau of the Census (Record Group 29) that include listings for your particular state and county. These schedules are digitized and available using the Catalog. See NARA’s 1940 Census Records web page for more information. Also, the 1940 U.S. Federal Census is available online for free through FamilySearch and Ancestry.
Please review the FamilySearch wiki for Naturalization Terms and Acronyms.
Beginning on September 27, 1906, the responsibility for naturalization proceedings was transferred to the Federal courts. If a naturalization took place in a Federal court, naturalization indexes, declarations of intention (with any accompanying certificates of arrival), and petitions for naturalization will usually be in the custody of the National Archives facility serving the state in which the Federal court is located. Unfortunately, no central index exists. To ensure a successful request, please include the name of petitioner (including known variants); date of birth; approximate date of entry to the US; approximate date of naturalization; where the individual was residing at the time of naturalization (city/county/state); and country of origin.
In most cases, the National Archives will not have a copy of the certificate of citizenship. Two copies of the certificate were created – one given to the petitioner as proof of citizenship, and one forwarded to the Immigration and Naturalization Service (INS).
Certificates of citizenship were issued by the Federal courts until October 1991 when INS took over responsibility for naturalization proceedings. All INS records are now overseen by the US Citizenship and Immigration Services (USCIS). USCIS maintains duplicate copies of court records (including the certificate of citizenship) created since September 27, 1906 and may be requested through the USCIS Genealogy Program.
We hope this is helpful. Best of luck with your family research!