Calvin the Zombie refers to two of Calvin's alter egos. They appeared in a story arc and a Sunday strip.
4/27 through 4/30 1987
Calvin the Zombie was originally featured, and named in the 4/27 through 4/30 1987 story arc. There, Calvin was pretending to be a reanimated corpse in order to avoid having to do his homework: in his words, "The living dead don't need to solve problems". Hobbes went on to imitate Calvin upon seeing his expression.
School Alter Egos
Calvin the Zombie also appeared in among the School Alter Egos as a blue-skinned, stitched-up version of Calvin escaping from a grave at night. Calvin the Zombie was analogous to Calvin's perceiving his experience at school as brain-numbing.