We present CO ( 1–0 ) observations of objects within the Shocked POststarburst Galaxy Survey taken with the Institut de Radioastronomie Millimétrique ( IRAM ) 30m single dish and the Combined Array for Research for Millimeter Astronomy ( CARMA ) interferometer . Shocked Poststarburst Galaxies ( SPOGs ) represent a transitioning population of galaxies , with deep Balmer absorption ( EW _ { H \delta } > 5Å ) , consistent with an intermediate-age ( A-star ) stellar population , and ionized gas line ratios inconsistent with pure star formation . The CO ( 1–0 ) subsample was selected from SPOGs detected by the Wide-field Infrared Survey Explorer with 22 \mu m flux detected at a signal-to-noise ( S/N ) > 3 . Of the 52 objects observed in CO ( 1–0 ) , 47 are detected with S/N > 3 . A large fraction ( 37–46 \pm 7 % ) of our CO-SPOG sample were visually classified as morphologically disrupted . The H _ { 2 } masses detected were between 10 ^ { 8.7 - 10.8 } M _ { \odot } , consistent with the gas masses found in normal galaxies , though approximately an order of magnitude larger than the range seen in poststarburst galaxies . When comparing the 22 \mu m and CO ( 1–0 ) fluxes , SPOGs diverge from the normal star-forming relation , having 22 \mu m fluxes in excess of the relation by a factor of \langle \epsilon _ { MIR } \rangle = 4.91 ^ { +0.42 } _ { -0.39 } , suggestive of the presence of active galactic nuclei ( AGN ) . The Na i D characteristics of CO-SPOGs show that it is likely that many of these objects host interstellar winds . Objects with the large Na i D enhancements also tend to emit in the radio , suggesting possible AGN-driving of neutral winds .