  JSNS$^2$ (J-PARC Sterile Neutrino Search at J-PARC Spallation Neutron Source)
is an experiment which searches for sterile neutrinos via the observation of
$\bar{\nu}_{\mu} \to \bar{\nu}_{e}$ appearance oscillations using muon
decay-at-rest neutrinos. The data taking of JSNS$^2$ have been performed from
2021. In this manuscript, a study of the accidental background is presented.
The rate of the accidental background is (9.29$\pm 0.39) \times 10^{-8}$ /
spill with 0.75 MW beam power and comparable to the number of searching
signals.
