Nonplanar chiral aromatic molecules are candidates for use as building blocks of multidimensional switching devices because the pi electrons can generate ring currents with a variety of directions. We employed (P)-2,2'-biphenol because four patterns of pi-electron rotations along the two phenol rings are possible and theoretically determine how quantum switching of the it-electron rotations can be realized. We found that each rotational pattern can be driven by a coherent excitation of two electronic states under two conditions: one is the symmetry of the electronic states and the other is their relative phase. On the basis of the results of quantum dynamics simulations, we propose a quantum control method for sequential switching among the four rotational patterns that can be performed by using ultrashort overlapped pump and dump pulses with properly selected relative phases and photon polarization directions. The results serve as a theoretical basis for the design of confined ultrafast switching of ring currents of nonplanar molecules and further current-induced magnetic fluxes of more sophisticated systems.