And it should be said here, those denied naturalization on the basis of race were not exempt, if they met all other conditions. Knowing this may also save researchers time looking for records.
Women & Children
In the U.S. from 1855 to 1922, by law, a women assumed the citizenship of her husband, whether immigrant non-citizen or American-born — it was not a matter of choice. This meant a woman marrying a U.S. citizen, either native born or naturalized became a citizen without application — and without documentation. Widowed women and their minor children could derive citizenship from a deceased husband, if he was in the process of naturalization before death. Conversely, American-born women marrying foreign nationals lost their citizenship, but again, no paper work. In the earliest days of the country, immigrant women could, in theory become naturalized, but few did. In 1802, women could gain naturalization through marriage by taking an oath of allegiance and renouncing former citizenship, but in 1855 the oath was no longer required and women simply assumed the citizenship of their husbands.
For that period between 1802 and 1855, the only documentation would be an oath of allegiance. After 1855, no documentation was required. For widows and their children, the only documentation is oath of allegiance. After 1922, women could apply on their own. In 1929, women who had gained citizenship through their husbands could apply for a Certificate of Derivative Citizenship by showing proof of marriage to a U.S. citizen prior to 1922
Derivative citizenship was no secret — it was well established and part of the culture; even so, there were exceptions to the rule. Some married women did apply and some naturalizations were granted; others were granted and revoked — all of which left a paper trail, so if you feel strongly that your female ancestor did apply, it never hurts to check with the local courts in the places where your ancestor lived (NARA Women and Naturalization). As a general rule, married women did not apply. But it is good to keep in mind, a woman may have derived citizenship from her father, before marriage.
As with married women, minor children assumed the citizenship of their fathers (after 1922, either parent). In the period between 1790 - 1940, researchers will find no naturalization records for children, with some exception. Between the years 1824 and 1906 a minor child who had lived in the country for at least 5 years prior to his 23rd birthday and whose father had not become naturalized, was permitted to file a Declaration of Intention and Petition for Naturalization (typically on one form), at the same time, without the usual waiting period. After 1929, children who had derived citizenship could file for a Certificate of Citizenship, and many did.
Although the rules were different, there were other groups of people who gained citizenship with little or no documentation, among them those serving in the military.
Citizenship was often used as an enticement, encouraging immigrants to apply for military service. Service did not grant citizenship automatically, but did make it easier. In general, beginning with the Civil War, veterans could file a petition for naturalization (second papers) after only one year of residency, skipping the declaration of intention (first papers). Some of these records may be among an immigrant's Alien Case File (A-File). It is said "almost 200,000 aliens were naturalized at U.S. military bases or in courts close to those bases before being sent overseas to fight during World War I" (NARA Coast to Coast). Others filed petitions after the war. So for this group, you should be able to find petitions and final, certificates of naturalization, if they continued through to completion.
Collective Naturalization
Citizenship could also be conferred on groups of people through an act of Congress following the acquisition of territories, as with the Louisiana Purchase, resulting in no individual documentation. And "Native Americans became U.S. citizens through collective naturalization in 1924" (Naturalization Terms).
As with other races, Native Americans were considered non-citizens. Prior to 1924 individual Native Americans were granted citizenship variously by other means such as land allotment or by marriage. Indians on reservation were citizens of their respective tribe were not taxed and could not vote. The land allotment allowed Indians into the mainstream (although they still could not vote in some states) where they could work and pay taxes.
Other groups denied citizenship African Americans were given the right to citizenship after the Civil War, but did not in reality obtain the right to vote until much later. And while the Chinese were gain to citizenship in 1943, that right was not extended to all Asians until 1952 the race question was off the books.
References
"NARA Coast to Coast: Naturalization, part 2." National Archives. 20 Sep. 2010. Web. Accessed 15 Jan. 2012.
"Women and Naturalization." National Archives: Prologue Magazine, Summer 1998, Vol. 30: 2. Web. Accessed 15 Jan 2012.
"Naturalization." Wikipedia, the Free Encyclopedia. Web. Accessed 15 Jan. 2012.
"Naturalization Act of 1790." Wikipedia, the Free Encyclopedia. Web. Accessed 15 Jan. 2012.
"Naturalization Terms and Acronyms." FamilySearch WIKI. Web. Accessed 15 Jan 2012.