  Leptonic flavor-changing $H^0$ decays with branching ratios of the order of
$10^{-5}-10^{-6}$ may constitute an interesting framework when looking for
large $CP$-violating effects. We show that leptonic $CP$~asymmetries of an
intermediate $H^0$ boson can be fairly large in natural scenarios of the
minimal Standard Model ($SM$) with right-handed neutrinos, at a level that may
be probed at future $H^0$~factories.
