We present polarization maps of NGC2071IR from thermal dust emission at 1.3 mm and from CO J= 2 \rightarrow 1 line emission . The observations were obtained using the Berkeley-Illinois-Maryland Association array in the period 2002-2004 . We detected dust and line polarized emission from NGC2071IR that we used to constrain the morphology of the magnetic field . From CO J= 2 \rightarrow 1 polarized emission we found evidence for a magnetic field in the powerful bipolar outflow present in this region . We calculated a visual extinction A _ { v } \approx 26 mag from our dust observations . This result , when compared with early single dish work , seems to show that dust grains emit polarized radiation efficiently at higher densities than previously thought . Mechanical alignment by the outflow is proposed to explain the polarization pattern observed in NGC2071IR , which is consistent with the observed flattening in this source .