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The nature of the companion stars in Type Ia Supernova (SNe) progenitorsystems remains unclear. One possible way to discriminate between differentscenarios is the presence (or absence) of circumstellar material, the leftovers from the progenitor evolution that may be revealed by their interactionwith the SN. A new method to probe the circumstellar environment has beenexploited for the normal Type Ia SN 2006X, leading for the first time to thedirect detection of material which escaped the progenitor system. In this paperwe apply the same analysis to the peculiar Type Ia SN 2000cx, with the aim ofconstraining the properties of its progenitor system. Using multi-epoch,high-resolution spectroscopy we have studied the spectral region where narrow,time-variable NaID absorption features are expected in case circumstellarmaterial is present along the line of sight. No NaID absorption is detected inthe rest-frame of the host galaxy to a level of a few mA, setting a stringentupper limit to the column density of the absorbing material (N(NaI)<=2 x 10^10cm-2). In this respect the peculiar Type Ia SN 2000cx is different from thenormal Ia SN 2006X. Whether this is to be attributed to a different progenitorsystem, to viewing-angle effects or to a low metallicity remains to beclarified.

Upper limit for circumstellar gas around the Type Ia SN 2000cx