In two-Higgs doublet models (and particularly in the MSSM) the CP-even (H) and CP-odd (A) neutral scalars are nearly degenerate in mass, and their s-channel production would lead to nearly overlapping resonances. CP-violating effects may connect these two Higgs bosons, giving origin to one-loop particle mixing, which, due to their mass proximity, can be resonantly enhanced, altering their lineshape significantly. We show that, in general, the effect of such a CP-violating mixing cannot be mimicked by (or be re-absorbed into) a simple redefinition of the H and A masses in the context of a CP-conserving model. Specifically, the effects of the CP-mixing are such that, either the mass-splitting of the H and A bosons lies outside the range allowed by the theory in the absence of CP-mixing, and/or the detailed energy dependence of the produced lineshape is clearly different from the one obtained by redefining the masses, but not allowing any mixing.