We present the polarization detections in DR21 ( OH ) from both the thermal dust emission at 1.3 mm and the CO J =2 \rightarrow 1 line obtained with the Berkeley-Illinois-Maryland Association ( BIMA ) array . Our results are consistent with the prediction of the Goldreich-Kylafis effect that the CO polarization is either parallel or perpendicular to the magnetic field direction . The detection of the polarized CO emission is over a more extended region than the dust polarization , while the dust polarization provides an aide in resolving the ambiguity of the CO polarization . The combined results suggest that the magnetic field direction in DR21 ( OH ) is parallel to the CO polarization and therefore parallel to the major axis of DR21 ( OH ) . The strong correlation between the CO and dust polarization suggests that magnetic fields are remarkably uniform throughout the envelope and the cores . The dispersion in polarization position angles implies a magnetic field strength in the plane of the sky of about 1 mG , compared with about 0.5 mG inferred for the line-of-sight field from previous CN Zeeman observations . Our CO data also show that both MM1 and MM2 power high-velocity outflows with v \gtrsim 25 km s ^ { -1 } relative to the systematic velocity .