  We calculate the complete differential decay distributions for the $B$ meson
decays, $\bar B \to D^{(*)} \ell \bar{X}$, to a massive right-handed (RH)
neutrino in the low-energy effective field theory (LEFT) framework. We find
that a massive RH neutrino does not introduce any new angular structures
compared to the massless case, but can cause significant distortions in angular
observables. We study the phenomenology of low-energy four-fermion operators
permitted by the standard model effective field theory (SMEFT) extended with RH
neutrinos (SMNEFT). We show that to explain the positive value of the
difference in forward-backward asymmetries, $\Delta A_{\text{FB}}\equiv
A_{\text{FB}}^\mu-A_{\text{FB}}^e$, tentatively inferred from Belle data, the
RH neutrino must be massive. We also make predictions for $q^2$ dependent
angular observables to motivate future measurements.
