  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 $b \to s \mu^+ \mu^-$ 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 $B \to
K^{(*)} \mu^+ \mu^-$. 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 $b \to s \mu^+ \mu^-$ processes are concerned. In this
single LQ model, the weak phase of the coupling can be large, leading to some
sizeable CP asymmetries in $B \to K^{(*)} \mu^+ \mu^-$. There is a spectrum of
$Z'$ models; the key parameter is $g_L^{\mu\mu}$, which describes the strength
of the $Z'$ coupling to $\mu^+\mu^-$. If $g_L^{\mu\mu}$ is small (large), the
constraints from $B^0_s$-${\bar B}^0_s$ 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 $B \to K^{(*)} \mu^+ \mu^-$ can indeed distinguish among NP $b \to s \mu^+
\mu^-$ models
