We study an extension of the Standard Model (SM) in which two copies of the SM Higgs doublet are added to the scalar sector. These extra doublets do not develop a vacuum expectation value, hence, they are textit{inert}. This essentially leads to a 3-Higgs Doublet Model (3HDM) with 2 inert and 1 active scalar doublets, which we denote as I(2+1)HDM. We allow for CP-violation in the textit{inert} sector, where the lightest textit{inert} state is protected from decaying to SM particles through the conservation of a $Z_2$ symmetry, so that it is a Dark Matter (DM) candidate. For this scenario, we identify a smoking gun signature of dark CP-violation in the form of production thresholds of pairs of textit{inert} neutral Higgs bosons at an $e^+e^-$ collider.
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