  We study an extension of the Standard Model (SM) in which two copies of the
SM scalar $SU(2)$ doublet which do not acquire a Vacuum Expectation Value
(VEV), and hence are \textit{inert}, are added to the scalar sector. 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. The lightest neutral particle from the
\textit{inert} sector, which has a mixed CP-charge due to CP-violation, is
hence a Dark Matter (DM) candidate. We discuss the new regions of DM relic
density opened up by CP-violation, and compare our results to the CP-conserving
limit and the Inert Doublet Model (IDM). We constrain the parameter space of
the CP-violating model using recent results from the Large Hadron Collider
(LHC) and DM direct and indirect detection experiments.
