We present a study of the polarizing power of the dust in cold dense regions ( dark clouds ) compared to that of dust in the general interstellar medium ( ISM ) . Our study uses new polarimetric , optical , and spectral classification data for 36 stars to carefully study the relation between polarization percentage ( p ) and extinction ( A _ { V } ) in the Taurus dark cloud complex . We find two trends in our p - A _ { V } study : ( 1 ) stars background to the warm ISM show an increase in p with A _ { V } ; and ( 2 ) the percentage of polarization of stars background to cold dark clouds does not increase with extinction . We detect a break in the p - A _ { V } relation at an extinction 1.3 \pm 0.2 mag , which we expect corresponds to a set of conditions where the polarizing power of the dust associated with the Taurus dark clouds drops precipitously . This breakpoint places important restrictions on the use of polarimetry in studying interstellar magnetic fields .