  Decays of charmonia(-like) particles with definite $J^{PC}$ (e.g.
${{\chi_{c{\rm 1}}}(3872)}$), to a ${{D}^{0}}{\overline{{D}}{}^{0}}$ system and
any combination of $C$-definite decay particles, are sources of
quantum-correlated ${{D}^{0}}{\overline{{D}}{}^{0}}$ systems with $C = P = \pm
1$. Methods to separate the $C = \pm1$ ${{D}^{0}}{\overline{{D}}{}^{0}}$
components from ${{\chi_{c{\rm 1}}}(3872)}$ decay samples are presented.
Studying $T$ and $CPT$ conservation in $C = +1$
${{D}^{0}}{\overline{{D}}{}^{0}}$ allows a final state reconstructibility
advantage. Several production mechanisms offer opportunities to collect $C =
+1$ ${{D}^{0}}{\overline{{D}}{}^{0}}$ systems.
