We explore a scenario of New Physics entering the description of B → K ( * ) µµ decay through couplings to the operators O 9,10 , satisfying C 9 = −C 10 . From the current data on B(Bs → µµ) and B(B → Kµµ) [15,22]GeV 2 , we obtain constraints on ReC 10 and ImC 10 which we then assume to be lepton specific, and find RK = B(B → Kµµ)/B(B → Kee) [1,6]GeV 2 = 0.88(8), consistent with recent value measured at LHCb. A specific realization of this scenario is the one with a scalar leptoquark state ∆, in which C 10 is related to the mass of ∆ and its Yukawa couplings. We then show that this scenario does not make any significant impact on Bs − Bs mixing amplitude nor to B(B → Kνν). Instead, it can modify RK * = B(B → K * µµ)/B(B → K * ee) [1,6]GeV 2 , which will soon be experimentally measured and we find it to be RK * = 1.11(8), while RK * /RK = 1.27(19). A similar ratio of forward-backward asymmetries also becomes lower than in the Standard Model.