An apparatus comprises a changeover mechanism which is able to change a connection state to any one of three states, i.e., “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 a transmission output shaft and the electric motor output shaft, and “a neutral connection state” in which no transmission path therebetween is provided. At a timing (time t1) at which a both-neutral-state is required during the vehicle is running, both “an operation for a changeover of the state-of-connecting of the clutch mechanism (C/T 30) from a connection-state to a shut-off-state” and “an operation for a changeover of said connection state of the changeover mechanism 50 from either one of the IN-Connection State and the OUT-Connection State to the non-connection state” are simultaneously started.