Neutron scattering cross sections and angular distributions represent one of the most glaring sources of uncertainty in calculations of nuclear systems. Even simple nuclei like $^{12}\mathrm{C}$ show indications of errors in nuclear databases for scattering reactions. Measurements of inelastic neutron scattering have historically measured either the scattered neutrons or the nuclear deexcitation $\ensuremath{\gamma}$ emission. Only a very small number of experiments attempted correlated measurements of both the neutron and $\ensuremath{\gamma}$ data simultaneously, even though these $n\text{\ensuremath{-}}\ensuremath{\gamma}$ correlations could be essential for understanding particle transport in nuclear systems. In this work we describe a measurement of the $n, \ensuremath{\gamma}$, and correlated $n\text{\ensuremath{-}}\ensuremath{\gamma}$ angular distributions from the $Q=4.4398 \mathrm{MeV}$ $^{12}\mathrm{C}(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction in a single experiment using an EJ-309 liquid scintillator detector array with wide angular coverage, and with a continuous incident neutron energy range from 6.5 to 16.5 MeV. We also provide a thorough covariance description of these results, including normalization of the probability distribution. While the measured $n$ distributions agree well with the relatively large number of available literature measurements, there are comparatively very few measurements of the $\ensuremath{\gamma}$ distributions from this reaction. However, our data support the presence of a nonzero ${a}_{4}$ Legendre polynomial component of the $\ensuremath{\gamma}$ angular distribution suggested in past measurements, which is currently not incorporated in the ENDF/B-VIII.0 library despite the use of these same literature data for evaluation of the $^{12}\mathrm{C}(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ cross section. The correlated $n\text{\ensuremath{-}}\ensuremath{\gamma}$ distribution measurements are limited to three measurements at incident neutron energies near 14 MeV. Our results do not generally agree with any of these literature measurements. We observe clear indications of significant changes in the $n$ distribution for specific $\ensuremath{\gamma}$-detection angles and vice versa especially near thresholds for other reaction channels, which shows the potential for significant bias in experiments that, for example, tag on inelastic scattering using a single or small number of $\ensuremath{\gamma}$-detection angles and could impact particle transport calculations.
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