The charge-current-induced spin polarization is a key property of topological insulators for their applications in spintronics. However, topological surface states are expected to give rise to only one type of spin polarization for a given current direction, which has been a limiting factor for spin manipulations. Here we report that in devices based on the bulk-insulating topological insulator BiSbTeSe2, an unexpected switching of spin polarization was observed upon changing the chemical potential. The spin polarization expected from the topological surface states was detected in a heavily electron-doped device, whereas the opposite polarization was reproducibly observed in devices with low carrier densities. We propose that the latter type of spin polarization stems from topologically-trivial two-dimensional states with a large Rashba spin splitting, which are caused by a strong band bending at the surface of BiSbTeSe2 beneath the ferromagnetic electrode used as a spin detector. This finding paves the way for realizing the spin transistor operation in future topological spintronic devices.