  Using $e^+e^-$ annihilation data of $2.93~\mathrm{fb}^{-1}$ collected at
center-of-mass energy $\sqrt{s}=3.773$ GeV with the BESIII detector, we measure
the absolute branching fraction of $D^{0}\to K^{-}\mu^{+}\nu_{\mu}$ with
significantly improved precision: ${\mathcal B}_{D^{0}\to
K^{-}\mu^{+}\nu_{\mu}}=(3.413\pm0.019_{\rm stat.}\pm0.035_{\rm syst.})\%$.
Combining with our previous measurement of ${\mathcal B}_{D^0\to K^-e^+\nu_e}$,
the ratio of the two branching fractions is determined to be ${\mathcal
B}_{D^0\to K^-\mu^+\nu_\mu}/{\mathcal B}_{D^0\to
K^-e^+\nu_e}=0.974\pm0.007_{\rm stat.}\pm0.012_{\rm syst.}$, which agrees with
the theoretical expectation of lepton flavor universality within the
uncertainty. A study of the ratio of the two branching fractions in different
four-momentum transfer regions is also performed, and no evidence for lepton
flavor universality violation is found with current statistics. Taking inputs
from global fit in the standard model and lattice quantum chromodynamics
separately, we determine $f_{+}^{K}(0)=0.7327\pm0.0039_{\rm
stat.}\pm0.0030_{\rm syst.}$ and $|V_{cs}| = 0.955\pm0.005_{\rm
stat.}\pm0.004_{\rm syst.}\pm0.024_{\rm LQCD}$.
