  In this paper, we analyze the possible anomalous $tcZ$ coupling effects in
the $b \to s $ mediated decays $\bar B \to \bar K^* \mu^+ \mu^-$ and $B_s \to
\mu^+ \mu^-$. After exploiting the available experimental data, the combined
constraints on the anomalous coupling $X_{ct}^L$ are derived. It is found that,
the bound on the magnitude $|X_{ct}^L|$ is dominated by the branching ratios of
these two decays. Furthermore, one sign-flipped solution is excluded by the
longitudinal fraction of $\bar B \to \bar K^* \mu^+ \mu^-$ at the low dilepton
mass region. After considering the combined constraints, for general complex
coupling $X_{ct}^L$, the predicted upper bound on $\mathcal B (t \to cZ)$ are
compatible with that from the recent CMS direct search. In particular, for the
case of real coupling $X_{ct}^L$, the upper bound reads $\mathcal B (t \to
cZ)<1.0\times 10^{-4}$, which is much lower than the current CMS bound but
still accessible at the LHC. With improved measurements at the LHC, the colser
correlations between the $t \to cZ$ and $b \to s$ mediated (semi-) leptonic
decays are expected in the near future.
