An apparatus comprises a changeover mechanism which is able to change a connection state of an electric motor output shaft to any one from alternatives consisting of “an IN-Connection State” in which a power transmission path is provided between a transmission input shaft and the electric motor output shaft, “an OUT-Connection State” in which a power transmission path is provided between the transmission output shaft and the electric motor output shaft, and “a neutral state” in which no transmission path therebetween is provided. The changeover is carried out based on a combination (area) of a vehicle speed V and a required driving torque T. As for the changeover, a neutral area is enlarged so that a possibility of selecting the neutral state becomes higher, as a battery temperature is higher, or as an electric motor temperature is higher, or as a remaining battery level is larger.