  Light sterile neutrinos can be probed in a number of ways, including
electroweak decays, cosmology and neutrino oscillation experiments. At
long-baseline experiments, the neutral-current data is directly sensitive to
the presence of light sterile neutrinos: once the active neutrinos have
oscillated into a sterile state, a depletion in the neutral-current data sample
is expected since they do not interact with the $Z$ boson. This channel offers
a direct avenue to probe the mixing between a sterile neutrino and the tau
neutrino, which remains largely unconstrained by current data. In this work, we
study the potential of the DUNE experiment to constrain the mixing angle which
parametrizes this mixing, $\theta_{34}$, through the observation of
neutral-current events at the far detector. We find that DUNE will be able to
improve significantly over current constraints thanks to its large statistics
and excellent discrimination between neutral- and charged-current events.
