  We study the relationship between the scale-height of the molecular gas disc
and the turbulent velocity dispersion of the molecular interstellar medium
within a simulation of a Milky Way-like galaxy in the moving-mesh code Arepo.
We find that the vertical distribution of molecular gas can be described by a
Gaussian function with a uniform scale-height of ~50 pc. We investigate whether
this scale-height is consistent with a state of hydrostatic balance between
gravity and turbulent pressure. We find that the hydrostatic prediction using
the total turbulent velocity dispersion (as one would measure from kpc-scale
observations) gives an over-estimate of the true molecular disc scale-height.
The hydrostatic prediction using the velocity dispersion between the centroids
of discrete giant molecular clouds (cloud-cloud velocity dispersion) leads to
more-accurate estimates. The velocity dispersion internal to molecular clouds
is elevated by the locally-enhanced gravitational field. Our results suggest
that observations of molecular gas need to reach the scale of individual
molecular clouds in order to accurately determine the molecular disc
scale-height.
