When a driver of a vehicle issues a command to stop an engine, an in-vehicle unit communicates with a portable device. When collation of ID codes of the in-vehicle unit and the portable device is OK, a collation ECU permits stopping of the engine. When the result of ID-code collation is NG, the ECU prohibits stopping of the engine. When a vehicle passenger has taken out the portable device from a vehicle compartment, once the engine of the vehicle is stopped, the engine can no longer be restarted. By prohibiting the stop of the engine based on the NG result of ID-code collation, however, it is possible to prevent a state in which the engine cannot be restarted. It is preferred to allow starting of the engine irrespective of the ID code collation, when the ECU stores an engine stall occurring previously.