An apparatus comprises a changeover mechanism which is able to change a connection state of an electric motor output shaft to any one of states including, “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 of a vehicle speed V and a required driving torque T. When the vehicle starts to drive, “the IN-Connection State” is selected. After the start of the vehicle and while the vehicle speed V is increasing, the changeovers to “the OUT-Connection State”, “the IN-Connection State”, and “the neutral state” are sequentially carried out.