A person became a naturalized citizen of the United States after having first filed his intention to do so and disavowing all allegiance to a foreign power. In Kentucky, the intention was filed in county court or circuit court and recorded in the court order books (court minutes). The information in the declarations might vary, but usually included the name of the person, date he filed his petition for naturalization and to whom he formerly vowed allegiance. Here is an example of a petition for naturalization:
“To the Honorable the Judge of the Lyon County Court from petitioner Adam Zollinger, a native of Germany State of Seittzien [?] and now under the dominion of Prussia, would respectfully state he was born in the
state Country of
Germany State of Seittzien, that he emigrated to the United States of America
in the year 1842 and landed at Baltimore in the State of Maryland in the year
1842, that he is 57 years of age and has resided in Kentucky about 28 years
last past, that it is and has been for three years last past bona fide his
intention to become a citizen of the United States of America and absolutely and
entirely renounces and [illegible] all allegiance and fidelity to any and every
foreign Prince, Potentate, State and Sovereignty whatsoever, and particularly
to King William now having dominion over Germany and Prussia to whom he now
owes allegiance. [signed] Adam Zollinger.
Subscribed and sealed before me by Adam Zollinger this August 26, 1872. J.L. Stubbs, Clerk Lyon County Court.”
Perhaps Adam Zollinger forgot that he had already filed his naturalization intention in another county, but at the next term of court, just a few days after filing the above intention, he withdrew his intention and report and stated he had filed an earlier petition for naturalization at the June 1844 term of Caldwell County, Kentucky Circuit Court. Since almost 30 years had passed sine the first petition was filed, two citizens of Lyon County made oaths that Zollinger had resided in Kentucky during that time and that had “behaved as a man of good moral character…” Zollinger was then granted all the rights and privileges of a naturalized citizen of the United States of America. 
 Lyon County, Kentucky Court Order Book B, p. 438, Monday, 26 Aug 1872, Naturalization Intention of Adam Zollinger.
 Lyon County, Kentucky Court Order Book B, p. 444, Monday, 23 Sep 1872, Naturalization Record of Adam Zollinger.
Published 23 April 2020, Western Kentucky Genealogy Blog, http://wkygenealogy.blogspot.com/