The lepton flavor universality violating (LFUV) measurements RK and RK∗ in B meson decays can be accounted for in non-universal Z′ models. We constrain the couplings of these Z′ models by performing a global fit to correlated b→ sℓℓ and b→ dℓℓ processes, and calculate their possible implications for Bs→ K¯ ∗ℓℓ observables. For real new physics (NP) couplings, the 1σ favored parameters allow the corresponding LFUV ratio RK∗(s) in Bs→ K¯ ∗ℓℓ to range between 0.8 and 1.2 at low q2. Complex NP couplings improve the best fit only marginally, however they allow a significant enhancement of the branching ratio, while increasing the range of RK∗(s)at low q2 to 0.8–1.8. We find that NP could cause zero-crossing in the forward–backward asymmetry AFB to shift towards lower q2 values, and enhancement in the magnitude of integrated AFB. The CP asymmetry ACP may be suppressed and even change sign. The simultaneous measurements of integrated RK∗(s)and ACP values to 0.1 and 1% respectively, would help in constraining the effective NP Wilson coefficient C9 in b→ dμμ interactions. © 2020, The Author(s).