Coherent thermal emission for a given polarization has been observed in many metamaterials with micro/nanostructures. Emissivity is typically obtained based on the equivalence between absorptivity and emissivity according to Kirchhoff's law; however, such a relationship may be invalid for nonreciprocal media. This study aims at developing a more general approach, without the constraint of optical reciprocity, that is applicable to magneto-optical materials and magnetic Weyl semimetals. A polarimetric analysis is theoretically carried out based on fluctuation electrodynamics to provide a complete description of the emissivity for all polarization states. The Stokes parameters are calculated from the coherency matrix for a multilayered system, which may include anisotropic media and even nonreciprocal materials. It is demonstrated that thermal emission may be circularly or linearly polarized in selected directions and frequencies. The findings of this work are consistent with the modified Kirchhoff's law provided by several groups in recent years, and therefore, justify the appropriateness of both the direct and indirect methods. This study will help the design of desired thermal emitters for energy harvesting and thermal control.