A control apparatus for a vehicle, the vehicle including: a driving force source; at least one drive wheel; a first transmission mechanism provided on a first power transmission path, the first power transmission path being defined between the driving force source and the drive wheel; a second transmission mechanism provided on a second power transmission path, the second power transmission path being defined between the driving force source and the drive wheel, the second transmission mechanism being provided in parallel with the first transmission mechanism; a first clutch mechanism configured to transmit power or interrupt transmission of power in the first power transmission path; and a second clutch mechanism configured to transmit power or interrupt transmission of power in the second power transmission path, the second clutch mechanism being a dog clutch equipped with a synchromesh mechanism, the control apparatus comprising: an electronic control unit configured to (a) when the electronic control unit switches transmission of power from the first transmission path to the second transmission path while the vehicle is traveling, actuate the second clutch mechanism and the first clutch mechanism such that the second clutch mechanism engages from a released state and then the first clutch mechanism is released, and (b) when the electronic control unit switches the transmission of power from the first transmission path to the second transmission path in a state where the vehicle is stopping or is stationary and in a state where power of the driving force source is transmitted to the drive wheel via the first transmission mechanism, actuate the first clutch mechanism and the second clutch mechanism such that the first clutch mechanism is released and the second clutch mechanism engages from a released state. a driving force source; at least one drive wheel; a first transmission mechanism provided on a first power transmission path, the first power transmission path being defined between the driving force source and the drive wheel; a second transmission mechanism provided on a second power transmission path, the second power transmission path being defined between the driving force source and the drive wheel, the second transmission mechanism being provided in parallel with the first transmission mechanism; a first clutch mechanism configured to transmit power or interrupt transmission of power in the first power transmission path; and a second clutch mechanism configured to transmit power or interrupt transmission of power in the second power transmission path, the second clutch mechanism being a dog clutch equipped with a synchromesh mechanism, the control apparatus comprising: an electronic control unit configured to (a) when the electronic control unit switches transmission of power from the first transmission path to the second transmission path while the vehicle is traveling, actuate the second clutch mechanism and the first clutch mechanism such that the second clutch mechanism engages from a released state and then the first clutch mechanism is released, and (b) when the electronic control unit switches the transmission of power from the first transmission path to the second transmission path in a state where the vehicle is stopping or is stationary and in a state where power of the driving force source is transmitted to the drive wheel via the first transmission mechanism, actuate the first clutch mechanism and the second clutch mechanism such that the first clutch mechanism is released and the second clutch mechanism engages from a released state. (a) when the electronic control unit switches transmission of power from the first transmission path to the second transmission path while the vehicle is traveling, actuate the second clutch mechanism and the first clutch mechanism such that the second clutch mechanism engages from a released state and then the first clutch mechanism is released, and (b) when the electronic control unit switches the transmission of power from the first transmission path to the second transmission path in a state where the vehicle is stopping or is stationary and in a state where power of the driving force source is transmitted to the drive wheel via the first transmission mechanism, actuate the first clutch mechanism and the second clutch mechanism such that the first clutch mechanism is released and the second clutch mechanism engages from a released state.