  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 vs. metallicity, we used the
derived specific energies and actions (E, J$_{r}$, J$_{\phi}$, J$_{z}$) to
cluster them into Chemo-Dynamically 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 intra-cluster dispersions in [Fe/H],
$[\text{C}/\text{Fe}]_{c}$ (evolution corrected carbon), and [Mg/Fe] when
compared to the intra-cluster dispersions of randomly clustered Group I CEMP
stars. In contrast, the Group II (primarily CEMP-no) stars exhibit clear
similarities in their intra-cluster abundances, with very low, statistically
significant, dispersions in $[\text{C}/\text{Fe}]_{c}$. 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 a 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.
