  A direct search for the standard model Higgs boson, H, produced in
association with a vector boson, V (W or Z), and decaying to a charm quark pair
is presented. The search uses a data set of proton-proton collisions
corresponding to an integrated luminosity of 35.9 fb$^{-1}$, collected by the
CMS experiment at the LHC in 2016, at a centre-of-mass energy of 13 TeV. The
search is carried out in mutually exclusive channels targeting specific decays
of the vector bosons: W $\to$ $\ell \nu$, Z $\to$ $\ell\ell$, and Z $\to$
$\nu\nu$, where $\ell$ is an electron or a muon. To fully exploit the topology
of the H boson decay, two strategies are followed. In the first one, targeting
lower vector boson transverse momentum, the H boson candidate is reconstructed
via two resolved jets arising from the two charm quarks from the H boson decay.
A second strategy identifies the case where the two charm quark jets from the H
boson decay merge to form a single jet, which generally only occurs when the
vector boson has higher transverse momentum. Both strategies make use of novel
methods for charm jet identification, while jet substructure techniques are
also exploited to suppress the background in the merged-jet topology. The two
analyses are combined to yield a 95% confidence level observed (expected) upper
limit on the cross section $\sigma$(H) $\mathcal{B}$(H $\to$
$\mathrm{c\bar{c}}$) of 4.5 (2.4 $^{+1.0}_{-0.7}$) pb, corresponding to 70 (37)
times the standard model prediction.
