  The Aharonov-Casher (AC) effect for quantum motion of a neutral magnetized
particle in the electric field is believed to be a topological effect closely
related to the known Aharonov-Bohm (AB) effect. We study how it depends on the
spin of the particle involved. Duality of the AB and AC effects is demonstrated
to exist only for two extreme spin (and magnetic moment) projections.
  Classical consideration confirms the conclusion. Motion of a classical
magnetized particle with generally oriented magnetic moment in the AC field
appears to be subjected to both forces and torques. Only for two special
orientations of the magnetic moment (same as in the quantum case) the motion is
effectively free and similar to the AB motion of a charged particle. Thus, the
AC effect is not really topological.
  Presence of higher multipoles totally destroys the possible AB-AC duality.
