The effects of a Lorentz symmetry-violating background vector on Aharonov-Casher scattering in the nonrelativistic limit are considered. Using the selfadjoint extension method, we find that there is additional scattering for any value of the self-adjoint extension parameter and non-zero energy bound states for negative values of this parameter. Expressions for the energy bound states, phase-shift and scattering matrix are explicitly determined in terms of the self-adjoint extension parameter. The expression obtained for the scattering amplitude reveals that the helicity is not conserved in this scenario.