[en] Having in mind its future extension for theoretical investigations related to charmed nuclei, we develop a relativistic formalism for the nonmesonic weak decay (NMWD) of single-Λ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the $(\mathrm{\pi <!--\; ??\; -->},K)$ one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of ${}_{\mathrm{\Lambda <!--\; ??\; -->}}^{12}\mathrm{C}$ are presented and compared with those obtained in the analogous nonrelativistic calculation. There is satisfactory agreement between the two approaches, and the only noteworthy difference is that the ratio ${\mathrm{\Gamma <!--\; ??\; -->}}_n/{\mathrm{\Gamma <!--\; ??\; -->}}_p$ is appreciably higher and closer to the experimental value in the relativistic calculation. The ability of describing existing data, including the most recent ones, on NMWD of Λ-hypernuclei, warrants application of the formalism to evaluate similar decay processes in charmed nuclei. (paper)