  The Double Helix Nebula (DHN), located 100 pc above Sgr A* in the Galactic
center (GC), is a unique structure whose morphology suggests it is a magnetic
feature (Morris, Uchida & Do 2006). Recent molecular observations toward the
DHN by Enokiya et al. (2014) revealed two candidate molecular counterparts of
the DHN at radial velocities of -35 km/s and 0 km/s and discussed the model in
which the DHN has its origin at the circumnuclear disk in the GC. In this
paper, new CO observations toward the DHN using the CSO and Mopra telescopes
are presented. The higher-resolution observations of ~1 pc scale reveal the
detailed distributions and kinematics of the two CO counterparts (the 0 km/s
and -35 km/s features) and provide new information on their physical
conditions. As a result, we find that the 0 km/s feature with a mass of
3.3x10^4 Msun coincides with the infrared emission of the DHN, indicating clear
association with the DHN. The association of the -35 km/s feature, with a mass
of 0.8x10^4 Msun, is less clear compared with the 0 km/s feature, but the
complementary distribution between the molecular gas and the DHN and velocity
variation along the DHN support its association with the DHN. The two molecular
features are highly excited, as shown by the relatively high CO J=2-1/J=1-0
intensity ratios of ~1.0, and have kinetic temperatures of ~30 K, consistent
with the typical molecular clouds in the GC.
