  The nature of the companion stars in Type Ia Supernova (SNe) progenitor
systems remains unclear. One possible way to discriminate between different
scenarios is the presence (or absence) of circumstellar material, the left
overs from the progenitor evolution that may be revealed by their interaction
with the SN. A new method to probe the circumstellar environment has been
exploited for the normal Type Ia SN 2006X, leading for the first time to the
direct detection of material which escaped the progenitor system. In this paper
we apply the same analysis to the peculiar Type Ia SN 2000cx, with the aim of
constraining 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 circumstellar
material is present along the line of sight. No NaID absorption is detected in
the rest-frame of the host galaxy to a level of a few mA, setting a stringent
upper limit to the column density of the absorbing material (N(NaI)<=2 x 10^10
cm-2). In this respect the peculiar Type Ia SN 2000cx is different from the
normal Ia SN 2006X. Whether this is to be attributed to a different progenitor
system, to viewing-angle effects or to a low metallicity remains to be
clarified.
