We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field.This neutral particle is also under the influence of a background that breaks the Lorentz symmetry.We focus on the Lorentz symmetry violation background determined by a space-like vector field.Then,we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential.Furthermore,we obtain the bound state solutions to the Schr(o)dinger-Pauli equation and show that the spectrum of energy is a function of the Aharonov-Casher geometric quantum phase.Finally,we discuss the arising of persistent spin currents.