Prior to 1990 "any court of record" could accept applications and issue citizship papers.  Residency in that court's district was not a requirement.  So one should check all three levels:county courts, state courts and federal courts.

All searches should begin in the National Archives.  Start with the regional office

The U.S. Citizenship and Imigration Services  has copies of all the records from all levels filed after September 26, 1906   C-Files include all US naturalizations from all States and Territories, and from all courts (Federal, State, and local). C-Files contain a copy of the Declaration of Intention to become a US Citizen (to 1952), Petition for Naturalization, and Certificate of Naturalization.

Declarations filed after Sept 27, 1906, were only good for 7 years. If the immigrant did not  petition within the 7 years, the declaration expired and the immigrant had to start over again from the beginning.     Most C-Files from 1906 to 1956 are on microfilm, with the remainder in paper form, and BCIS has an index to those that have been filmed. They are available with a Freedom of Information/Privacy Act request to BCIS Headquarters in Washington, D.C. For naturalization records after 1956, Freedom of Information requests must be sent to the appropriate  District Office

USCIS also holds records relationg to "derivative" citizenship, reumed or restored U.S. Citizenship and loss of U.S. citizenship. 

The USCIS Genealogy Program is a fee-for-service program providing family historians and other researchers with timely access to historical immigration and naturalization records of deceased immigrants. (Brochure)

Pre-1906 the records are only found in the National Archives or the individual courts.

Another good source of information are the applications for U. S. Passports. and Arriving Passenger Lists.

History Highlights:

Race, Sex and Age Distinctions