  Diagnosing core of supernova requires favor-dependent reconstruction of three
species of neutrino spectra, \nu_e, \bar{\nu}_{e} and \nu_x (a collective
notation for \nu_{\mu}, \bar{\nu}_{\mu}, \nu_{\tau}, and \bar{\nu}_{\tau}). We
point out that, assuming the information available, CPT symmetry can be tested
with supernova neutrinos. We classify all possible level crossing patterns of
neutrinos and antineutrinos into six cases and show that half of them contains
only the CPT violating mass and mixing patterns. We discuss how additional
informations from terrestrial experiments help identifying CPT violation by
narrowing down the possible flux patterns. Although the method may not be good
at precision test, it is particularly suited to uncover gross violation of CPT
such as different mass patterns of neutrinos and antineutrinos. The power of
the method is due to the nature of level crossing in supernova which results in
the sensitivity to neutrino mass hierarchy and to the unique characteristics of
in situ preparation of both \nu and \bar{\nu} beams. Implications of our
discussion to the conventional analyses with CPT conservation are also briefly
mentioned.
