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The nonleptonic decays ${B}_{d,s}\ensuremath{\rightarrow}{K}^{*0}{\overline{K}}^{*0}$ are reanalyzed in perturbative QCD approach, which is based on the ${k}_{\mathrm{T}}$ factorization. In Standard Model, calculated branching fraction and longitudinal polarization of ${B}_{d}\ensuremath{\rightarrow}{K}^{*0}{\overline{K}}^{*0}$ agreement with experimental measurements, while predictions ${B}_{s}\ensuremath{\rightarrow}{K}^{*0}{\overline{K}}^{*0}$ cannot agree data simultaneously. parameter that combines fractions to be ${L}_{{K}^{*}{\overline{K}}^{*0}}^{\mathrm{PQCD}}={12.7}_{\ensuremath{-}3.2}^{+5.6}$, also larger than extracted from measurements. We then study all observables by introducing a family nonuniversal ${Z}^{\ensuremath{'}}$ boson $b\ensuremath{\rightarrow}sq\overline{q}$ transitions. order reduce number new parameters, we simplify model as possible. It found fixed value ${\ensuremath{\omega}}_{{B}_{s}}=0.55$, these exists space where including fraction, ${L}_{{K}^{*}{\overline{K}}^{*0}}$-parameter, could accommodated All our results small further tested running LHC experiment, Belle-II, future high-energy colliders.