Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the N=(1,1) Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the N=1 model but we find new solutions with a time-like Killing vector that are absent in the N=1 case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the

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... called rotating hairy BTZ black holes and logarithmic black holes in an AdS_3 background. Furthermore, we show that under certain assumptions there is no supersymmetric Lifshitz black hole solution.