That's a tough one, Bill. Traditionally, Arkansas has been credited with about 45,000 Confederate and about 13,000 Union soldiers. However, research done over the last 30 years or so demonstrate that the number of Arkansas Confederate soldiers has been understated, and the number of Arkansas Union soldiers has been overstated.
Arkansas regiments organized for U.S. service included large numbers of men from Missouri and elsewhere. Recent estimates put the number of actual Arkansas residents in Union regiments at something more like about 9,000 -- the balance being "furriners".
Confederate numbers have been understated for several reasons. First, men who enlisted after March 1, 1864, to the end of the war are not included. Also not included are men who served in the State troops, State militia, home guards, etc., as well as the large number of Arkansans who served in regiments from Missouri, Tennessee, Texas, Louisiana and the Indian Territory. Of course, to balance this off, it must be remembered that some soldiers were counted twice -- those serving in Arkansas regiments east of the Mississippi and exchanged back in Arkansas, who subsequently served in Arkansas regiments in the Trans-Mississippi Department.
The database of Arkansas Confederate soldiers I've put together over the years, taking into account the factors I mentioned above, contains well over 50,000 names -- but I'm still actively engaged in resolving a large number of "mystery men", some of whom may be men from surrounding border states.