  The anisotropy of velocities in MHD turbulence is demonstrated explicitly by
calculating the velocity gradients as a function of direction in representative
simulations of decaying turbulence. It follows that the optical depths of
spectral lines are anisotropic when there is MHD turbulence, and that this
anisotropy influences the polarization characteristics of the emergent
radiation. We calculate the linear polarization that results for the microwave
lines of the CO molecule in star-forming gas and show that it is comparable to
the polarization that is observed. This and our earlier result--that the
anisotropy of MHD turbulence may be the cause for the absence of the Zeeman
$\pi $-components in the spectra of OH mainline masers--are the first
demonstrations of the occurrence of anisotropy in the optical depths caused by
MHD turbulence. A non-local approximation is developed for the radiative
transfer and the results are compared with those from a local (LVG)
approximation.
