Control device and control method for vehicle power transmission device

When an engine stop control is executed while an automatic ratio shift portion (20) is in a neutral state, a switching clutch (C0) is operated, so that a differential portion carrier (CA0) of a differential portion planetary gear device (24) that is linked to an engine (8), and a differential portion ring gear (R0) linked the automatic ratio shift portion (20) are integrally rotated. Therefore, along with the engine stop control, the rotation speed of the rotating elements of the differential portion planetary gear device (24) is reduced while the rotating elements are integrally rotated or substantially integrally rotated. Since the rotating elements are rotated integrally or substantially integrally, the high rotation speed of the differential portion ring gear (R0) linked to the automatic ratio shift portion (200, which tends to have a heightened rotation speed particularly during the neutral state, is prevented.