  The muon decay-at-rest ($\mu$-DAR) facility provides us with an ideal
platform to probe purely muonic charged-current nonstandard neutrino
interactions (NSIs). We propose to probe this class of NSI effects using
antineutrinos from a $\mu$-DAR source in conjunction with neutrinos from the
future Tokai to Kamioka superbeam experiment with megaton Hyper Kamiokande
detector (T2HK). Even though muonic NSIs are absent in neutrino production at
T2HK, we show that our proposed hybrid setup comprising $\mu$-DAR and T2HK
helps in alleviating the parameter degeneracies that can arise in data.
Analytic considerations reveal that the oscillation probability is most
sensitive to the NSI parameter in the $\mu$-e sector. For this parameter, we
show that the $\mu$-DAR setup can improve on the existing bounds down to around
0.01, especially when the data are combined with neutrino data from T2HK
experiment due to the lifting of parameter degeneracies. The high precision
with which $\mu$-DAR can measure $\delta_{\rm{CP}}$ is shown to be robust even
in the presence of the considered NSIs. Finally, we show that the combination
of $\mu$-DAR along with T2HK can also be used to put mild constraints on the
NSI phase in the vicinity of the maximal CP-violating value for the chosen
benchmark value of $\varepsilon^{\mu e}_{\mu e}=0.01$.
