  We present a search for eV-scale sterile neutrino oscillations in the
MicroBooNE liquid argon detector, simultaneously considering all possible
appearance and disappearance effects within the $3+1$ active-to-sterile
neutrino oscillation framework. We analyze the neutrino candidate events for
the recent measurements of charged-current $\nu_e$ and $\nu_{\mu}$ interactions
in the MicroBooNE detector, using data corresponding to an exposure of
6.37$\times$10$^{20}$ protons on target from the Fermilab booster neutrino
beam. We observe no evidence of light sterile neutrino oscillations and derive
exclusion contours at the $95\%$ confidence level in the plane of the
mass-squared splitting $\Delta m^2_{41}$ and the sterile neutrino mixing angles
$\theta_{\mu e}$ and $\theta_{ee}$, excluding part of the parameter space
allowed by experimental anomalies. Cancellation of $\nu_e$ appearance and
$\nu_e$ disappearance effects due to the full $3+1$ treatment of the analysis
leads to a degeneracy when determining the oscillation parameters, which is
discussed in this paper and will be addressed by future analyses.
