We present an analysis comparing the properties of 45 giant molecular clouds (GMCs) in M33 and the atomic hydrogen (HI) with which they are associated. High-resolution VLA observations are used to measure the properties of HI in the vicinity of GMCs and in regions where GMCs have not been detected. The majority of molecular clouds coincide with a local peak in the surface density of atomic gas, though 7% of GMCs in the sample are not associated with high-surface density atomic gas. The mean HI surface density in the vicinity of GMCs is 10 M_sol/pc^2 and tends to increase with GMC mass as Sigma_HI ~ M_GMC^0.27. 39 of the 45 HI regions surrounding GMCs have linear velocity gradients of ~0.05 km/s/pc. If the linear gradients previously observed in the GMCs result from rotation, then 53% are counterrotating with respect to the local HI. If the linear gradients in these local HI regions are also from rotation, 62% are counterrotating with respect to the galaxy. If magnetic braking reduced the angular momentum of GMCs early in their evolution, the angular velocity of GMCs would be roughly one order of magnitude lower than what is observed. Based on our observations, we consider the possibility that GMCs may not be rotating. Atomic gas not associated with GMCs has gradients closer to 0.03 km/s/pc, suggesting that events occur during the course of GMC evolution that may increase the shear in the atomic gas.
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