  We present polarization observations in DR21(OH) from thermal dust emission
at 3 mm and from CO J=1-0 line emission. The observations were obtained using
the Berkeley-Illinois-Maryland Association array. Previous observations of this
region at 1.3 mm for the polarized continuum emission, and also the CO J=2-1
polarized emission have been made before. Our continuum polarization results
are consistent with those results. However, the direction of the linear
polarization for the J=1-0 is perpendicular to that of the CO J=2-1
polarization. This unexpected result was explored by obtaining numerical
solutions to the multilevel, radiative transfer equations for a gas with
anisotropic optical depths. We find that in addition to the anisotropic optical
depths, anisotropic excitation due to a source of radiation that is external to
the CO is needed to understand the orthogonality in the directions of
polarization. The continuum emission by dust grains at the core of DR21(OH) is
sufficient to provide this external radiation. The CO polarization must arise
in relatively low density (nH2 ~ 100 [cm^-3]) envelope gas. We infer B ~ 10
[micro Gauss] in this gas, which implies that the envelope is subcritical.
