  In 2016, the Atomki collaboration discovered an anomaly in the decay of
beryllium excited states that matched theoretical predictions for an unknown
force-carrying boson. We suggest a search for such a hypothesized `dark photon'
over the same parameter space to be carried out at the Mu3e detector. We
discuss the mechanisms by which a dark photon may be observed, and outline the
details of this detector experiment. We extrapolate on this groundwork to
analyze projections for the sensitivity of the experiment. Additionally, we
quantify the expected precision of the measurements and how the resulting data
would indicate the existence of a dark photon. Finally, we discuss potential
challenges of the proposed search at Mu3e.
