One man who was definitely carried on the rolls as deserting both armies was
Henry Morton Stanley. As to the state he was from....
the United Kingdom is a state and he was born in Wales with the birth name of John Rowlands. In fact, he deserted several "states he was from".
Rowlands allegedly was adopted by an American named Stanley in New Orleans LA and that presumably made him a citizen of the
state of Louisiana. He left that state and went to the
state of Arkansas where he eventually signed up in July 1861 with the 6th Arkansas, Capt. Smith's "Dixie Greys" company, under the name
William H Stanley.
He was captured at Shiloh, April 1862. He thereupon
deserted Arkansas and the CSA (as they would regard it) and became a galvanized Yankee known as
Henry M Stanley (
one of his military cards records he joined "The Irish Brigade"!!!!). He
deserted his Union regiment from hospital and was officially listed as having done so on August 31, 1862.
Having made his way to Liverpool only to be rejected by his mother, he returned to the USA,
joined the Union Navy and deserted them February 10th 1865 in Portsmouth NH.
Source:
http://www.historynet.com/henry-morton-stanley-goes-to-war.htm
He abandoned his state of birth in 1885, only to desert his adopted country state and re-up with the old one:
Stanley married Dorothy Tennant on July 12, 1890, and they adopted a son, Denzil. Stanley was renaturalized a British subject in 1892 (he had become a U.S. citizen on May 15, 1885)
Source:
https://www.britannica.com/biography/Henry-Morton-Stanley
Edit - Well, your response brings up two separate arguments with the wording of the question.
The question asked players to name the "state" from which the individual came. You argue that the United Kingdom should be considered to be a "state." Although the questioner evidently intended that "state" should be taken to mean one of the United States (or Confederate States), I will accept your argument in regard to the United Kingdom.
The question also asked players to name someone who "deserted" from both armies. You named someone who was originally captured and joined the other side to escape captivity, then deserted from the other side's forces.
MRB1863, in post # 8, cites the case of William Dawson, who did the same thing. The source that he posted indicates that, although Dawson was originally considered to have deserted, the charge of desertion was ultimately dropped as the result of an act of Congress more than a decade after the war was over.
However, since those who became "Galvanized" after being taken prisoner were evidently considered to be deserters at one time, I will accept your answer.
Hoosier