CIT 6 is a carbon star in the transitional phase from the asymptotic giant branch (AGB) to the protoplanetary nebulae (pPN). Observational evidences of two point sources in the optical, circumstellar arc segments in an HC$_3$N line emission, and a bipolar nebula in near-infrared provide strong support for the presence of a binary companion. Hence, CIT 6 is very attractive for studying the role of companions in the AGB-pPN transition. We have carried out high resolution $^{12}$CO $J=2-1$ and $^{13}$CO $J=2-1$ observations of CIT 6 with the Submillimeter Array combined with the Submillimeter Telescope (single-dish) data. The $^{12}$CO channel maps reveal a spiral-shell pattern connecting the HC$_3$N segments in a continuous form, and an asymmetric outflow corresponding to the near-infrared bipolar nebula. Rotation of the $^{12}$CO channel peak position may be related to the inner spiral winding and/or the bipolar outflow. An eccentric orbit binary is suggested for the presences of an anisotropic mass loss to the west and a double spiral pattern. The lack of interarm emission to the west may indicate a feature corresponding to the periastron passage of a highly eccentric orbit of the binary. Spatially-averaged radial and spectral profiles of $^{12}$CO $J=2-1$ and $^{13}$CO $J=2-1$ are compared with simple spherical radiative transfer models, suggesting a change of $^{12}$CO/$^{13}$CO abundance ratio from $sim30$ to $sim50$ inward in the CSE of CIT 6. The millimeter continuum emission is decomposed into extended dust thermal emission (spectral index $sim-2.4$) and compact emission from radio photosphere (spectral index $sim-2.0$).
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