  A search for exotic decays of the Higgs boson to a pair of light pseudoscalar
particles a$_1$ is performed under the hypothesis that one of the pseudoscalars
decays to a pair of opposite sign muons and the other decays to
b$\overline{\mathrm{b}}$. Such signatures are predicted in a number of
extensions of the standard model (SM), including next-to-minimal supersymmetry
and two-Higgs-doublet models with an additional scalar singlet. The results are
based on a data set of proton-proton collisions corresponding to an integrated
luminosity of 35.9 fb$^{-1}$, accumulated with the CMS experiment at the CERN
LHC in 2016 at a centre-of-mass energy of 13 TeV. No statistically significant
excess is observed with respect to the SM backgrounds in the search region for
pseudoscalar masses from 20 GeV to half of the Higgs boson mass. Upper limits
at 95% confidence level are set on the product of the production cross section
and branching fraction, $\sigma_{\mathrm{h}}\mathcal{B}$(h $\to$ a$_1$ a$_1$
$\to$ $\mu^+\mu^-\mathrm{b}\bar{\mathrm{b}}$), ranging from 5 to 33 fb,
depending on the pseudoscalar mass. Corresponding limits on the branching
fraction, assuming the SM prediction for $\sigma_{\mathrm{h}}$, are
(1$-$7)$\times$ 10$^{-4}$.
