  We study the nature and the origin of the dust arch in the halo of the
edge-on galaxy NGC 4631 detected by Neininger & Dumke (1999). We present CO
observations made using the new On-The-Fly mapping mode with the FCRAO 14m
telescope, and find no evidence for CO emission associated with the dust arch.
Our examination of previously published HI data shows that if previous
assumptions about the dust temperature and gas/dust ratio are correct, then
there must be molecular gas associated with the arch, below our detection
threshold. If this is true, then the molecular mass associated with the dust
arch is between 1.5 x 10^8 M(sun)and 9.7 x 10^8 M(sun), and likely towards the
low end of the range. A consequence of this is that the maximum allowed value
for the CO-to-H_2 conversion factor is 6.5 times the Galactic value, but most
likely closer to the Galactic value. The kinematics of the HI apparently
associated with the dust arch reveal that the gas here is not part of an
expanding shell or outflow, but is instead two separate features (a tidal arm
and a plume of HI sticking out into the halo) which are seen projected together
and appear as a shell. Thus there is no connection between the dust "arch" and
the hot X-ray emitting gas that appears to surround the galaxy Wang et al.
(2001).
