Absence of Spontaneous CP violation in Multi-Higgs Doublet Extension of MSSM

We show that in the multi-Higgs extension of minimal supersymmetric standard model, which has N-pairs of Higgs doublets (called NHMSSM), it is impossible to break CP spontaneously, if we do not allow for fine-tuning relations between parameters. The result holds true even in the presence of spontaneous R-parity breaking.