Turbulence is a crucial factor in many models of planet formation, but it has only been directly constrained among a small number of planet-forming disks. Building on the upper limits on turbulence placed in disks around HD 163296 and TW Hya, we present ALMA CO J = 2-1 line observations at ∼0″3 (20-50 au) resolution and 80 ms-1 channel spacing of the disks around DM Tau, MWC 480, and V4046 Sgr. Using parametric models of disk structure, we robustly detect nonthermal gas motions around DM Tau of between 0.25cs and 0.33cs, with the range dominated by systematic effects, making this one of the only systems with directly measured nonzero turbulence. Using the same methodology, we place stringent upper limits on the nonthermal gas motion around MWC 480 (<0.08cs) and V4046 Sgr (<0.12cs). The preponderance of upper limits in this small sample and the modest turbulence levels consistent with dust studies suggest that weak turbulence (α ≲ 10-3) may be a common, albeit not universal, feature of planet-forming disks. We explore the particular physical conditions around DM Tau that could lead this system to be more turbulent than the others.