Can the Higgs sector trigger CP violation in the MSSM?

We reanalyze the possibility of CP violation in the Higgs sector of the minimal supersymmetric standard model (MSSM). Contrary to the result of previous analysis, spontaneous CP violation cannot occur by only chargino and neutralino radiative corrections since the vacuum does not stable. Top and stop radiative corrections are crucially needed. However even with this correction there is no experimentally allowed region in tan β ≥ 1. This situation is not remedied even if the stop left-right mixing is included. We also analyze explicit CP violation in the Higgs sector of the MSSM and show that the effect is too small to influence the phenomenology. We thus show that the Higgs sector cannot, by itself, trigger CP violation in the MSSM.