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 $varepsilon^{mu e}_{mu e}=0.01$.
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