At present, there are several measurements of B decays that exhibit discrepancies with the predictions of the SM, and suggest the presence of new physics (NP) in b → sµ + µ − transitions. Many NP models have been proposed as explanations. These involve the tree-level exchange of a leptoquark (LQ) or a flavor-changing Z boson. In this paper we examine whether it is possible to distinguish the various models via CP-violating effects in B → K ( * ) µ + µ − . Using fits to the data, we find the following results. Of all possible LQ models, only three can explain the data, and these are all equivalent as far as b → sµ + µ − processes are concerned. In this single LQ model, the weak phase of the coupling can be large, leading to some sizeable CP asymmetries in B → K ( * ) µ + µ − . There is a spectrum of Z models; the key parameter is g µµ L , which describes the strength of the Z coupling tos mixing are stringent (weak), leading to a small (large) value of the NP weak phase, and corresponding small (large) CP asymmetries. We therefore find that the measurement of CP-violating asymmetries in B → K ( * ) µ + µ − can indeed distinguish among NP b → sµ + µ − models.