  We investigate the prospects for detecting light leptophilic dark sectors
with a missing-momentum experiment at NA64 running in muon mode. In particular,
we consider models in which dark matter connects to the visible sector through
a lepton- or muon-specific scalar mediator. These scalars can also account for
the $\sim 3.5\sigma$ discrepancy between the measured and predicted values of
$(g-2)_{\mu}$ . We emphasize the complementarity between NA64-$\mu$ and other
terrestrial and astrophysical probes.
