Context: We investigate non-Zeeman circular polarization and linear polarization levels of up to 1% of $^{12}$CO spectral line emission detected in a shocked molecular clump around the supernova remnant (SNR) IC 443, with the goal of understanding the magnetic field structure in this source. Aims: We examine our polarization results to confirm that the circular polarization signal in CO lines is caused by a conversion of linear to circular polarization, consistent with anisotropic resonant scattering. In this process background linearly polarized CO emission interacts with similar foreground molecules aligned with the ambient magnetic field and scatters at a transition frequency. The difference in phase shift between the orthogonally polarized components of this scattered emission can cause a transformation of linear to circular polarization. Methods: We compared linear polarization maps from dust continuum, obtained with PolKa at APEX, and $^{12}$CO ($J=2rightarrow1$) and ($J=1rightarrow0$) from the IRAM 30-m telescope and found no consistency between the two sets of polarization maps. We then reinserted the measured circular polarization signal in the CO lines across the source to the corresponding linear polarization signal to test whether before this linear to circular polarization conversion the linear polarization vectors of the CO maps were aligned with those of the dust. Results: After the flux correction for the two transitions of the CO spectral lines, the new polarization vectors for both CO transitions aligned with the dust polarization vectors, establishing that the non-Zeeman CO circular polarization is due to a linear to circular polarization conversion.