Army Sgt. Ronald Evans Taylor, 28, was found dead late Oct. 14 after crashing his car into a house in Ogden.
Investigators said Taylor had been shot when they found his body in the wrecked vehicle.
Detectives said the composite picture was developed through witnesses.
Anyone with information regarding the case, including the identity or whereabouts of the man shown in the picture, may contact Detective Richard Lewis at (785) 537-2112, ext. 3050.
Taylor was a two-tour veteran of Iraq and the father of a young boy.