  We present a comprehensive study of the velocity dispersion of the atomic
(HI) and molecular (H2) gas components in the disks (R < R25) of a sample of 12
nearby spiral galaxies with moderate inclinations. Our analysis is based on
sensitive high resolution data from the THINGS (atomic gas) and HERACLES
(molecular gas) surveys. To obtain reliable measurements of the velocity
dispersion, we stack regions several kilo-parsecs in size, after accounting for
intrinsic velocity shifts due to galactic rotation and large-scale motions. We
stack using various parameters: the galacto-centric distance, star formation
rate surface density, HI surface density, H2 surface density, and total gas
surface density. We fit single Gaussian components to the stacked spectra and
measure median velocity dispersions for HI of 11.9 +/- 3.1 km/s and for H2 of
12.0 +/- 3.9 km/s. The CO velocity dispersions are thus, surprisingly, very
similar to the corresponding ones of HI, with an average ratio of
sigma(HI)/sigma(CO) = 1.0 +/- 0.2 irrespective of the stacking parameter. The
measured CO velocity dispersions are significantly higher (factor 2) than the
traditional picture of a cold molecular gas disk associated with star
formation. The high dispersion implies an additional thick molecular gas disk
(possibly as thick as the HI disk). Our finding is in agreement with recent
sensitive measurements in individual edge-on and face-on galaxies and points
towards the general existence of a thick disk of molecular gas, in addition to
the well-known thin disk in nearby spiral galaxies.
