There are many motivations for introducing new extra bosons to extend the standard model of particle physics.
If there exists a boson $X$ which is lighter than muon and neutral, the rare decay of muon, $\mu\to eX$, could happen.

In this article, we investigate the $\mu^-\to e^-X$ process in muonic atoms.
By calculating the spectrum of the emitted electron for several cases, the model-discriminating power is discussed.
We report the characteristic model-dependence of the spectrum near the endpoint, which implies that the future experiments using muonic atoms would be good probes for unknown invisible bosons.