Dvorak and Postle introduced DP-coloring of simple graphs as a generalization of list-coloring. They proved a Brooks' type theorem for DP-coloring; and Bernshteyn, Kostochka, and Pron extended it to DP-coloring of multigraphs. However, detailed structure, when a multigraph does not admit DP-coloring, was not specified. In this note, we make this point clear and give the complete structure. This is also motivated by the relation to signed coloring of signed graphs.