  I show that the CP-violating asymmetry in K^0 vs \bar{K}^0 \to
\pi^+\pi^-\pi^0 decays differs from that in K_L \to \pi^+\pi^-, K_L \to
\pi^0\pi^0 or the semileptonic K_L transitions, if there exists CPT violation
in K^0-\bar{K}^0 mixing. A delicate measurement of this difference at a super
flavor factory (e.g., the \phi factory) will provide us with a robust test of
CPT symmetry in the neutral kaon system.
