Two level calculations by others for the linear polarizations expected for molecular emission lines from interstellar clouds are extended by considering a number of coupled rotational states of a diatomic molecule. Higher transitions commonly have strengths comparable with that of the J=1-0 transition so that depolarization due to coupling between the various J-states might be expected to reduce the predicted linear polarization. The significance of the null observational results obtained recently by Wannier, Scoville and Barvainis is assessed. The inclusion of additional states tends to decrease the maximum polarizations, though the calculated polarization is increased under conditions for which “superthermal” excitation occurs.