  The potential for detecting DM at the Compact Linear Collider (CLIC) is
investigated at \mbox{$\sqrt{s}=$ 3 TeV}. The sensitivity of the search is
estimated by computing the 95\% confidence level upper limit cross section as a
function of the dark matter mass. Left-handed (right-handed) polarised \Pem
beams increase (decrease) respectively the Standard Model backgrounds and are
essential to characterize the WIMPs properties and control the systematic
errors. Using right-handed polarised \Pem beams is decreasing significantly the
95\% confidence level cross section. Using the ratio of the energy
distributions for left-handed and right-handed polarised \Pem beams, systematic
errors cancel out. Computing the 95\% confidence level upper limit cross
section using the ratio requires a model assumption to compute the expected
number of signal events. Exclusion limits for dark matter are derived using
dark matter Simplified Models for two values of the e-e-mediator vertex
coupling, a mediator width of 10 GeV and for a fixed value of the
mediator-DM-DM coupling. For a mediator mass of 3.5 TeV, the measurement of the
differential distribution of the significance as a function of the photon
energy for the process \mbox{\Pem \Pep $\to$ X X \PGg} allows the
discrimination between different dark matter mediators and the measurement of
the WIMP mass to nearly half the centre-of-mass energy. For a \mbox{1 TeV}
WIMP, the mass is determined with a 1\% accuracy.
