So the neutrality of both States was not respected by either side and for the most part was a sham. But the fact that they thought they could have declared and enforced their neutrality is the interesting point. At one point in 1862 the Governor of Arkansas threatened to seceed from the Confederacy, recall all the states volunteer troops and declare Arkansas as an independent state belonging to neither the United States not the Confederate States because of the appearent abandonment of the state by General Earl Van Dorn.
So again an example of this attitude that the States could act as independent governing bodies unto themselves. I doubt that Arkansas' independence from both the Confederacy and the Union would have been respected for a moment, but the threat was still there and the Richmond government reacted to that threat.