  We show that the CP-violating effect in K^0 vs \bar K^0-->\pi^+\pi^-\pi^0
decays differs from that in K_{\rm L}-->\pi^+\pi^-, K_{\rm L}-->\pi^0\pi^0 or
the semileptonic K_{\rm L} transitions, if there exists CPT violation in
K^0-\bar{K}^0 mixing. A delicate measurement of this difference in the KTeV
experiment and at the \phi factory will provide a new test of CPT symmetry in
the neutral kaon system.
