  We present a study of the nonmesonic weak decay (NMWD) of charmed hypernuclei
using a relativistic formalism. We work within the framework of the independent
particle shell model and employ a ($\pi$,$K$) one-meson-exchange model for the
decay dynamics. We implement a fully relativistic treatment of nuclear recoil.
Numerical results are obtained for the one-neutron-induced transition NMWD
rates of the $_{\Lambda^{+}_{c}}^{12}$N. The effect of nuclear recoil is
sizable and goes in the direction to decrease the nuclear decay rate. We found
that the NMWD decay rate of $_{\Lambda^{+}_{c}}^{12}$N is of the same order of
magnitude as the partial decay rate for the corresponding mesonic decay
$\Lambda^+_c \rightarrow \Lambda + \pi^+$, suggesting the feasibility of
experimental detection of such heavy-flavor nuclear processes.
