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 kiloparsec-scale observations) gives an overestimate 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.