  Models with extended quark sector affect the CP asymmetry in the $B\to \psi
K_{S}$ decay, $a_{\psi K_{S}}$, in two ways: First, the top-mediated box
diagram is not necessarily the only important contribution to $B-\bar{B}$
mixing. Second, the $3\times 3$ CKM matrix is no longer unitary. We analyze the
constraints that follow from the CDF measurement, $a_{\psi K_{S}}
=0.79^{+0.41}_{-0.44}$, on the mixing parameters of extended quark sectors.
Most noticeably, we find significant constraints on the phase of the relevant
flavor changing $Z$ coupling in models with extra down quarks in vector-like
representations. Further implications for the CP asymmetry in semileptonic $B$
decays are discussed.
