  JSNS$^2$ (J-PARC Sterile Neutrino Search at J-PARC Spallation Neutron Source)
is an experiment that is searching for sterile neutrinos via the observation of
$\bar{\nu}_{\mu} \rightarrow \bar{\nu}_e$ appearance oscillations using
neutrinos with muon decay-at-rest. For this search, rejecting
cosmic-ray-induced neutron events by Pulse Shape Discrimination (PSD) is
essential because the JSNS$^2$ detector is located above ground, on the third
floor of the building. We have achieved 95$\%$ rejection of neutron events
while keeping 90$\%$ of signal, electron-like events using a data driven
likelihood method.
