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We have measured the time-dependent decay rate for the process B ->
J/psi K*0(892) in a sample of about 88 million Upsilon(4S) ->
BBbar decays collected with the BaBar detector at the PEP-II
asymmetric-energy B Factory at SLAC. In this sample we study
flavor-tagged events in which one neutral B meson is reconstructed in
the J/psi K*0 or J/psi K*0bar final state. We measure
the coefficients of the cosine and sine terms in the time-dependent
asymmetries for J/psi K*0 and J/psi K*0bar, find them to
be consistent with the Standard Model expectations, and set upper limits
at 90% C.L. on the decay amplitude ratios |A (B0bar -> J/psi K*0)|/|A
(B0 -> J/psi K*0)| < 0.26 and |A (B0 -> J/psi K*0bar)|/|A (B0bar ->
J/psi K*0bar)| < 0.32. For a single ratio of wrong-flavor to favored
amplitudes for B0 and B0bar combined, we obtain an upper limit of 0.25 at
90% C.L.
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