  Motivated by the very recent measurements performed at the LHCb and the
Tevatron of the $B_s^0-\bar B_s^0$ mixing, in this paper we revisit it in a
family non-universal $Z^{\prime}$ model, to check if a simultaneous explanation
for all the mixing observables, especially for the like-sign dimuon charge
asymmetry observed by the D0 collaboration, could be made in such a specific
model. In the first scenario where the $Z^\prime$ boson contributes only to the
off-diagonal element $M_{12}^s$, it is found that, once the combined
constraints from $\Delta M_s$, $\phi_s$ and $\Delta \Gamma_s$ are imposed, the
model could not explain the measured flavour-specific CP asymmetry $a_{fs}^s$,
at least within its $1\sigma$ ranges. In the second scenario where the NP
contributes also to the absorptive part $\Gamma_{12}^s$ via tree-level
$Z^\prime$-induced $b\to c\bar{c}s$ operators, we find that, with the
constraints from $\Delta M_s$, $\phi_s$ and the indirect CP asymmetry in
$\bar{B}_d\to J/\psi K_S$ taken into account, the present measured $1\sigma$
experimental ranges for $a_{fs}^s$ could not be reproduced too. Thus, such a
specific $Z^\prime$ model with our specific assumptions could not
simultaneously reconcile all the present data on $B_s^0-\bar B_s^0$ mixing.
Future improved measurements from the LHCb and the proposed superB experiments,
especially of the flavour-specific CP asymmetries, are expected to shed light
on the issue.
