Fundamental CP-violating quantities in an SU(2)⊗U(1) model with many Higgs doublets

We consider an SU(2)⊗U(1) gauge theory with many scalar doublets, but without fermions. We devise a systematic method of constructing quantities which are invariant under changes of basis of the scalar fields, but acquire a minus sign under a general CP transformation. Those quantities provide a basis-independent way of checking for the existence of CP violation.