This story is from the Cincinnati Daily Enquirer of September 30, 1864. The jump into the river kind of reminds me of the circumstances behind Ambrose Bierce's short-story (and Twilight Zone episode) An Occurrence at Owl Creek Bridge, especially with its Civil War theme, though the authorities' struggles to keep the culprit under control brought to mind the Harrison Ford movie, The Fugitive
Covington News – Drafted Man Shot – “A few months ago, a citizen of this city, named James C. Blinn was drafted. He failed to report to duty, and was arrested as a deserter. While being conveyed to the rendezvous at Louisville, he made his escape from the guards who had him in charge, and nothing more was seen of him until about ten days ago, when he was re-arrested in Cincinnati, and again started to Louisville, hand-cuffed, and in charge of a guard of soldiers.
Just before the boat reached Louisville, he succeeded in slipping up his handcuffs and jumped overboard, but was shot and killed by the guard while in the water."