We construct a sample of 644 carbon-enhanced metal-poor (CEMP) stars with abundance analyses based on moderate- to high-resolution spectroscopic studies. Dynamical parameters for these stars are estimated based on radial velocities, Bayesian parallax-based distance estimates, and proper motions from Gaia EDR3 and DR3, supplemented by additional available information where needed. After separating our sample into the different CEMP morphological groups in the Yoon-Beers diagram of absolute carbon abundance versus metallicity, we used the derived specific energies and actions (E, Jr, Jph, Jz) to cluster them into Chemodynamically Tagged Groups (CDTGs). We then analyzed the elemental-abundance dispersions within these clusters by comparing them to the dispersion of clusters that were generated at random. We find that, for the Group I (primarily CEMP-s and CEMP-r/s) clustered stars, there exist statistically insignificant intracluster dispersions in [Fe/H], [C/Fe]c (evolution corrected carbon), and [Mg/Fe] when compared to the intracluster dispersions of randomly clustered Group I CEMP stars. In contrast, the Group II (primarily CEMP-no) stars exhibit clear similarities in their intracluster abundances, with very low, statistically significant, dispersions in [C/Fe]c and marginally significant results in [Mg/Fe]. These results strongly indicate that Group I CEMP stars received their carbon enhancements from local phenomena, such as mass transfer from an evolved binary companion in regions with extended star formation histories, while the CDTGs of Group II CEMP stars formed in low-metallicity environments that had already been enriched in carbon, likely from massive rapidly rotating ultra- and hyper-metal-poor stars and/or supernovae associated with high-mass early- generation stars.