Possibly it's a 37mm round for the light artillery / anti tank gun from early in the war period. That same caliber was carried by some light armor like the Stuart. Crossed cannons is the symbol for the Field Artillery Branch of the Army, assuming the crossed cannons you see are similar in shape to the tubes of a napoleanic gun.
In looking for other pics of WW2 37mm ammo I am not finding much similar to that. The semi rimmed base it just not quite right for most of the Army guns, they were typically rimmed cartridges. How long is the overall round? Can you get a measurement of it? That might help in pinning it down, possibly a round from the P39?