  We present a detailed analysis comparing the velocity fields in molecular
clouds and the atomic gas that surrounds them in order to address the origin of
the gradients. To that end, we present first-moment intensity-weighted velocity
maps of the molecular clouds and surrounding atomic gas. The maps are made from
high-resolution 13CO observations and 21-cm observations from the
Leiden/Argentine/Bonn Galactic HI Survey. We find that (i) the atomic gas
associated with each molecular cloud has a substantial velocity
gradient---ranging within 0.02 to 0.07 km/s/pc---whether or not the molecular
cloud itself has a substantial linear gradient (ii) If the gradients in the
molecular and atomic gas were due to rotation, this would imply that the
molecular clouds have less specific angular momentum than the surrounding HI by
a factor of 1-6. (iii) Most importantly, the velocity gradient position angles
in the molecular and atomic gas are generally widely separated---by as much as
130 degrees in the case of the Rosette Molecular Cloud. This result argues
against the hypothesis that molecular clouds formed by simple top-down collapse
from atomic gas.
