  We present high-spectral resolution M-band spectra from iSHELL on NASA's
Infrared Telescope Facility (IRTF) along the line of sight to the debris disk
host star HD 32297. We also present a Gemini Planet Imager (GPI) H-band
polarimetric image of the HD 131488 debris disk. We search for fundamental CO
absorption lines in the iSHELL spectra of HD 32297 but do not detect any. We
place an upper limit on the CO column density of $\sim$6$\times10^{15}$
cm$^{-2}$. By combining the column density upper limit, the CO mass measured
with ALMA, and the geometrical properties of the disk, we estimate the scale
height of the CO to be $\lesssim$ 2 au across the radial extent of the disk
($\sim$80-120 au). We use the same method to estimate the CO scale height of
three other edge-on, CO-rich debris disks that all have CO observed in
absorption with HST as well as in emission with ALMA: $\beta$ Pictoris, HD
110058, and HD 131488. We compare our estimated CO scale heights of these four
systems to the millimeter dust scale heights and find that, under the
assumption of hydrostatic equilibrium, there is a potential correlation between
the CO and millimeter dust scale heights. There are multiple factors that
affect the gas vertical structure such as turbulence, photodissociation with
weak vertical mixing, as well as where the gas originates. One possible
explanation for the potential correlation could be that the gas and dust are of
a similar secondary origin in these four systems.
