  The superconducting (SC) state ($T_\mathrm{c}$ = 0.3 K) of the heavy-fermion
compound CeRh$_2$As$_2$, which undergoes an unusual field-induced transition to
another high-field SC state, emerges from an unknown ordered state below
$T_\mathrm{o}$ = 0.55 K. While an electronic multipolar order of itinerant
Ce-4$f$ states was proposed to account for the $T_\mathrm{o}$ phase, the exact
order parameter has not been known to date. Here, we report on muon spin
relaxation ($\mu$SR) studies of the magnetic and SC properties in
CeRh$_2$As$_2$ single crystals at low temperatures. We reveal a magnetic origin
of the $T_\mathrm{o}$ order by identifying a spontaneous internal field below
$T_\mathrm{o}$ = 0.55 K. Furthermore, we find evidence of a microscopic
coexistence of local magnetism with bulk superconductivity. Our findings open
the possibility that the $T_\mathrm{o}$ phase involves both dipole and higher
order Ce-4$f$ moment degrees of freedom and accounts for the unusual non-Fermi
liquid behavior.
