  A CO\,2-1 line survey is performed toward a sample of 58 high Galactic
latitude post-AGB (pAGB) stars. To complement the observations, a compilation
of literature CO\,2-1 line data of known pAGB stars is done. After combining
the datasets, CO\,2-1 line data are available for 133 pAGB stars (about 34 per
cent of known pAGB stars) among which 44 are detections. The CO line strengths
are compared with infrared dust emission for these pAGB stars by defining a
ratio between the integrated CO\,2-1 line flux and {\it IRAS} 25\,mu flux
density (CO-IR ratio). The relationship between the CO-IR ratio and the {\it
IRAS} color C23 (defined with the 25 and 60\,mu flux densities) is called here
the CO-IR diagram. The pAGB objects are found to be located between AGB stars
and planetary nebulae (PNe), and segregate into three distinctive groups (I, II
and III) on the CO-IR diagram. By analyzing their various properties such as
chemical types, spectral types, binarity, circumstellar envelope expansion
velocities, and pAGB sub-types on the CO-IR diagram, it is argued that the
group-I objects are mainly intermediate mass C-rich pAGB stars in early pAGB
stage (almost all of the considered carbon rich `21\,mu' stars belong to this
group); the group-II objects are massive or intermediate mass pAGB stars which
already follow the profound trend of PNe; and the group-III objects are mainly
low mass binary pAGB stars with very weak CO\,2-1 line emission (almost all of
the considered RV\,Tau variables belong to this group). The CO-IR diagram is
proven to be a powerful tool to investigate the co-evolution of circumstellar
gas and dust during the short pAGB stage of stellar evolution.
