This event is mentioned in Tennal's History of Nemaha County in the section, The State of Kansas vs. Wilton Baughn. The case involved the pursuit of 4 horse thieves: Jackson, Strange, Baughn and Mooney. The posse arrested Jackson and Strange. However, Baughn and Mooney escaped on foot and were pursued. When Baughn and Mooney were confronted, Jesse Dennis was shot. Melvin Baughn, the chief offender, was arrested in 1867 in Leavenworth. Baughn was tried in 1868. Judge Graham ordered that Baughn be hanged on Sept. 18, 1868.
No further mention of this Mooney is mentioned in Tennal's history. There is a James Mooney that migrated from Illinois to Centralia in the 1880s -- about 20 years after the hanging.
While trying to locate information on this Mooney, another hanging involving a Mooney was found.
The article, History of Lynchings in Kansas, indicates that Daniel Mooney was hanged in 1863 in Atchison. Additional information on Mooney being hung in Atchison is available in the book, Lynchings in Kansas, 1850-s to 1932 by Harriet Frazier.
Picture from Wikimedia Commons -- https://commons.wikimedia.org/wiki/File:Horse_thief_hanging.png