Information about naturalization, while not usually a treasure trove for a genealogist, can be helpful in confirming or discovering a few facts: the county where an ancestor lived (especially helpful during the years between censuses), their year of immigration, and their complete and accurate full name. (Federal immigration records after 1906 provide much more information, but the vast majority of Norwegian-Americans in the Norwegian Ridge area immigrated prior to this date.) Not all immigrants would seek naturalization – not having citizenship restricted only the right to vote – but as it would automatically be conferred upon a spouse and foreign-born children, it was sometimes sought to confer an advantage to the family in later years.
The Minnesota Historical Society has an informative video explaining the process an immigrant would go through to achieve citizenship:
The three relevant records from the immigration process are called “Declaration of Intention” (or “first papers”), the “Petition for Naturalization” (or “second papers”) and finally the Certificate of Naturalization. Only the first two are generally available and helpful to researchers. County and state historical societies have microfilm copies of these records, which as you can predict are unindexed and very tedious to search. Ancestry.com has many of these records available for the Norwegian Ridge area but they are locked behind a high-priced paywall (you can probably use the site for free through your local library).
You can use the US Census records to help narrow down when an immigrant would have filed their second papers:
1870: Column 19, “Male Citizens of the United States of twenty-one years of age and upwards” would have an mark
1900 and 1910: The year of immigration is added. Columns 15 and 16, “Year of immigration to the U.S.” and “Whether naturalized or Alien” would be filled in using these codes:
AL Alien, not naturalized, and had not begun the naturalization process
PA The Declaration of Intent has been filed
NA Naturalized citizen
1920: The year of naturalization is added. Columns 13-15, “Year of immigration to the United States,” “Naturalized or alien,” and “If naturalized, year of naturalization.” The codes are the same as 1900-1910.
1930: Omits the year of naturalization. Columns 22-23, “Year of immigration to the United States” and “Naturalized or alien.” The codes are the same as 1900-1920.
1940: Column 16, “Citizenship of the foreign born.” Uses the same codes as 1930, with the addition of “Am Cit” for American Citizen.