Magnetic fields are expected to play an important role in accretion processes for circumstellar disks. Measuring the magnetic field morphology is difficult, especially since polarimetric (sub)millimeter continuum observations may not trace fields in most disks. The Goldreich-Kylafis (GK) effect suggests that line polarization is perpendicular or parallel to the magnetic field direction. We attempt to observe CO(2-1), $^{13}$CO(2-1), and C$^{18}$O(2-1) line polarization toward HD 142527 and IM Lup, which are large, bright protoplanetary disks. We use spatial averaging and spectral integration to search for signals in both disks, and detect a potential CO(2-1) Stokes $Q$ signal toward both disks. The total CO(2-1) polarization fractions are 1.57 $pm$ 0.18% and 1.01 $pm$ 0.10% for HD 142527 and IM Lup, respectively. Our Monte Carlo simulations indicate that these signals are marginal. We also stack Stokes parameters based on the Keplerian rotation, but no signal was found. Across the disk traced by dust of HD 142527, the 3$sigma$ upper limits for $P_{text{frac}}$ at 0.5$^{primeprime}$ ($sim$80 au) resolution are typically less than 3% for CO(2-1) and $^{13}$CO(2-1) and 4% for C$^{18}$O(2-1). For IM Lup, the 3$sigma$ upper limits for these three lines are typically less than 3%, 4%, and 12%, respectively. Upper limits based on our stacking technique are up to a factor of $sim$10 lower, though stacking areas can potentially average out small-scale polarization structure. We also compare our continuum polarization at 1.3 mm to observations at 870 $mu$m from previous studies. The polarization in the northern dust trap of HD 142527 shows a significant change in morphology and an increase in $P_{text{frac}}$ as compared to 870 $mu$m. For IM Lup, the 1.3 mm polarization may be more azimuthal and has a higher $P_{text{frac}}$ than at 870 $mu$m.
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