Thank you for posting on History Hub!
Naturalization is the process by which an alien becomes an American citizen. It is a voluntary act; naturalization is not required.
Prior to September 27, 1906, any "court of record" (municipal, county, state, or Federal) could grant United States citizenship. Often petitioners went to the court most geographically convenient for them. As a general rule, the National Archives does not have naturalization records created in state or local courts. However, a few indexes and records have been donated to the National Archives from counties, states, and local courts. Researchers should contact the National Archives facility serving the state in which the petitioner resided to determine if records from lower courts are available. In certain cases county court naturalization records maintained by the National Archives are available as microfilm publications. Records from state and local courts are often at state archives or county historical societies.
Beginning September 27, 1906, the responsibility for naturalization proceedings was transferred to the Federal courts. It took time for the lower courts to let go of the practice, so researchers may need to look at lower courts if the National Archives does not maintain a record of naturalization from the early-mid 20th century.
In general, naturalization was a two-step process* that took a minimum of five years. After residing in the United States for two years, an alien could file a "declaration of intention" ("first papers") to become a citizen. After three additional years, the alien could "petition for naturalization" (”second papers”). After the petition was granted, a certificate of citizenship was issued to the alien. These two steps did not have to take place in the same court. [*Exceptions can include cases of derivative citizenship, processes for minor aliens 1824-1906, and special consideration for veterans.]
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 National Archives facility serving the state in which the Federal court is located. No central index exists. To ensure a successful request with the National Archives researchers should 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).
Concerning your grandfather’s arrival, we searched the Access to Archival Databases (AAD) and located the Data Files Relating to the Immigration of Italians to the United States, documenting the period 1855 - 1900 in the Records of the Center for Immigration Research (Collection CIR) and located two Vincenzo Parcos, one 24 years old and the other 39, with the intended destinations being Pennsylvania. The 24 year old was a laborer and arrived in 1895 on the ship California, and the 39 year old was a farmer from Lago, Calabria who disembarked from Naples & Palermo, arriving in 1900 on the ship Archimede.
We hope this guidance serves you well, and good luck with your Italian endeavor!
If this 1930 census record is for your grandfather, it shoes that was was naturalized in 1905.