  In the light of new experimental results on $B \to K\pi$ decays, we study the
decay processes $B \to K \pi$ in the framework of both R-parity conserving
(SUGRA) and R-parity violating supersymmetric models. We find that any possible
deviations from the Standard Model indicated by the current data for the
branching ratios and the direct CP asymmetries of $B \to K\pi$ can be explained
in both R-parity conserving SUGRA and R-parity violating SUSY models. However,
there is a difference between the predictions of both models to the
time-dependent CP asymmetry observable $S_{K_{_S} \pi^0}$ whose current
experimental results include large uncertainties. We demonstrate that this
difference can be useful for testing both models with more accurate data for
$S_{K_{S} \pi^0}$ and $A_{CP}^{+-}$ in the near future.
