Single crystals of Cu4I4(CH3NHCS)2 and CuI(CH3NHCS)2 polymer complexes have been crystallized. Electrical conductivity and X-ray diffraction measurements have been performed on these compounds. The space group symmetries (monoclinic C2/m and triclinic P-1) and the crystal structures are determined at room temperature. It is suggested from the temperature dependence of the conductivity that these complexes become a proton superionic conductor gradually as the temperature is raised. The difference in the conductivity at high temperature between these compounds is discussed with the refined structures.