I've been trying to locate my great grandfather Saul Wilson's naturalization records for some time. His son Joseph Wilson, born in the Russian Empire, identified his citizenship as derivative (i.e., coming via his father's naturalization).  I have been unable to find Saul, however, in any extant naturalization index in any court in New York City. I have also gone through all the index cards microfilmed by the Family History Library for Columbia County, New York. The City of Hudson, where the family lived at least from 1898 to 1904 is in Columbia County.
The census records I have gathered for both the U.S. Federal Census (1900, 1920) and the New York State Census (1905, 1915) indicate that Saul was naturalized.  I suspect that Saul was naturalized before 1906 (therefore, the naturalization papers would likely be in a local court/archive rather than at the National Archives).
However, I have also contacted US Citizenship and Immigration Services genealogy program and asked them to look for any records on my grandfather Joseph Wilson's derivative citizenship. They had none.
So, I have been checking Voter Lists.  Before 1957, New York State voters had to register to vote annually. Voter lists will identify individuals, their addresses and party affiliations. Books of voter lists are organized by Assembly District within each New York City Borough. Google Books has the 1918 List of Enrolled Voters book for the Bronx.  I found my great grandparents in Assembly District 7.
They are listed as Saul and Hattie Wilson at 2086 Vyse ave - where they'd lived since at least 1917 and where they continued to live for the rest of their lives.
Seeing them in this book still does not tell me where and when Saul was naturalized, but it does tell me that they were, indeed, citizens.  With this information I will be able to contact the Bronx Board of Elections to see if they still have voter registration forms from that year or earlier. The registration forms may tell me the court in which and when they naturalized.
At first, it was surprising to see my great grandmother Hoda's name on the list. After all, women did not gain suffrage in the United States until 1920. In fact, however, women in the State of New York gained the right to vote in 1917. So, it appears, "Hattie" wasted no time getting to the voting booth.
1. "New York Passenger Lists, 1820-1957," digital images, Ancestry.com (http://www.ancestry.com : accessed 18 May 2008), manifest, Olympia, New York (10 February 1956) to New York, arriving 27 February 1956, List 20, passenger number 5, Joseph Wilson; citing National Archives Microfilm Serial T715, Microfilm Roll 8691.
2. On the 1910 U.S. Federal Census population schedule, the citizenship info for the family was left blank.
3. For a nice summary of NYC voter records see the JewishGen InfoFile:
4. Board of Elections of the City of New York, List of Enrolled Voters, 1918, Borough of the Bronx. Google Books (http://books.google.com/books : accessed 17 October 2013). Google Books also has 1919 and 1922 NYC Voter Lists.
5. Prior to 1922, women gained or lost citizenship based upon the status of their husbands. So, Hoda and their minor children (Nina, Joe and Ben) would have gained citizenship based upon Saul's naturalization. Their youngest child, Esther, was born in the United States and, therefore, born a citizen.