  We present a search for the decay of a B0 or B0bar meson to a K*0bar K0 or
K*0 K0bar final state, using a sample of approximately 232 million BBbar events
collected with the BABAR detector at the PEP-II asymmetric energy e+e- collider
at SLAC. The measured branching fraction is B(B0 --> K*0bar K0) + B(B0 --> K*0
K0bar) = (0.2+0.9-0.8+0.1-0.3)x 10-6. We obtain the following upper limit for
the branching fraction at 90% confidence level: B(B0 --> K*0bar K0) + B(B0 -->
K*0 K0bar) <1.9 x 10-6. We use our result to constrain the Standard Model
prediction for the deviation of the CP asymmetry in B0 --> phi K0 from
sin(2beta).
