  Using data taken during the year 2000 with the NA48 detector at the CERN SPS,
a search for the CP violating decay K_S -> 3 pi0 has been performed. From a fit
to the lifetime distribution of about 4.9 million reconstructed K0/K0bar -> 3
pi0 decays, the CP violating amplitude eta_000 = A(K_S -> 3 pi0)/A(K_L -> 3
pi0) has been found to be Re(eta_000) = -0.002 +- 0.011 +- 0.015 and
Im(eta_000) = -0.003 +- 0.013 +- 0.017. This corresponds to an upper limit on
the branching fraction of Br(K_S -> 3 pi0) < 7.4 x 10^-7 at 90% confidence
level. The result is used to improve knowledge of Re(epsilon) and the CPT
violating quantity Im(delta) via the Bell-Steinberger relation.
