We present CO(1-0) observations of objects within the Shocked POststarburst Galaxy Survey taken with the Institut de Radioastronomie Millimetrique (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 (Hdelta>5A), 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 22um 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%) of our CO-SPOG sample were visually classified as morphologically disrupted. The H2 masses detected were between 10^(8.7-10.8) Msuns, 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 22um and CO(1-0) fluxes, SPOGs diverge from the normal star-forming relation, having 22um fluxes in excess by a factor of <EMIR,SPOG>=4.91+0.42-0.39. 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.
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