  In this work we investigate the possibility to observe $C\!P$-violation in
$\eta$ decays containing muons at the proposed REDTOP experiment. Employing the
SMEFT to parametrize the new-physics $C\!P$-violating effects, we find that a
single operator exists for which is possible to observe $C\!P$-violation at
REDTOP in $\eta\to\mu^+\mu^-$ decays, while evading bounds from the neutron
electric dipole moment and $D^-\to\mu\bar{\nu}$
