  Quasiparticle states around a single vortex in a $p_x\pm i p_y$-wave
superconductor are studied on the basis of the Bogoliubov-de Gennes (BdG)
theory, where both charge and current screenings are taken into account. Due to
the violation of time reversal symmetry, there are two types of vortices which
are distinguished by their winding orientations relative to the angular
momentum of the chiral Cooper pair. The BdG solution shows that the charges of
the two types of vortices are quite different, reflecting the rotating Cooper
pair of the $p_x\pm i p_y$-wave paring state.
