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In this paper we investigate the influence of the leakage current on the performance of Silicon Drift Detectors. First, analytical considerations are given in order to highlight the problems, specific for this type of detector, that emerge with leakage current. Then the obtained results are compared with the data of laboratory measurements. Aiming at a mass production of SDDs for the Inner Tracking System of the ALICE experiment at LHC we propose a simple and fast measurement for a preliminary selection before passing to a detailed acceptance test.