Initials on census
You probably know this from working with the census but just in case... the initials on the census may confuse you. In the 1900, 1910, 1920, and 1930, the person's naturalization status is indicated by "AL" for alien, "PA" for first papers, and ""NA" for naturalization. Look for those initials. They will indicate whether you should look into the naturalization documents.