  We discuss the existence of elliptical polarisation in rotational spectral
lines of CO and other molecules within the context of the Anisotropic Resonant
Scattering (ARS) model. We show that the effect of ARS on the radiation field
can lead to not only the previously predicted transformation of background
linear polarisation into circular polarisation (i.e., Faraday conversion), but
also the occurrence of Faraday rotation and the generation of elliptically
polarised signals in an otherwise initially unpolarised radiation field. This
is due to a collective behaviour between the large number of molecules acting
as a diffraction ensemble that strongly favours forward scattering over any
other mode. Our application to astronomical data demonstrates the dependency of
the Stokes parameters on the strength and orientation of the ambient magnetic
field, and suggests that ARS will manifest itself for a wide range of molecular
species and transitions.
