We present CO observations of 78 spiral galaxies in local merger pairs. These galaxies represent a subsample of a Ks-band-selected sample consisting of 88 close major-merger pairs (HKPAIRs), 44 spiral-spiral (S+S) pairs, and 44 spiral-elliptical (S+E) pairs, with separation <20h^-1^kpc and mass ratio <2.5. For all objects, the star formation rate (SFR) and dust mass were derived from Herschel PACS and SPIRE data, and the atomic gas mass, MHI, from the Green Bank Telescope HI observations. The complete data set allows us to study the relation between gas (atomic and molecular) mass, dust mass, and SFR in merger galaxies. We derive the molecular gas fraction (M_H2_/M*), molecular-to-atomic gas mass ratio (M_H2_/M_HI_), gas-to-dust mass ratio and SFE (=SFR/M_H2_) and study their dependences on pair type (S+S compared to S+E), stellar mass, and the presence of morphological interaction signs. We find an overall moderate enhancement (~2x) in both molecular gas fraction (M_H2_/M*) and molecular-to-atomic gas ratio (M_H2_/M_HI_) for star-forming galaxies in major-merger pairs compared to non-interacting comparison samples, whereas no enhancement was found for the SFE nor for the total gas mass fraction ((MHI+MH2)/M^Cstar). When divided into S+S and S+E, low mass and high mass, and with and without interaction signs, there is a small difference in SFE, a moderate difference in M_H2_/M*, and a strong difference in M_H2_/M_HI_ between subsamples. For the molecular-to-atomic gas ratio M_H2_/M_HI_, the difference between S+S and S+E subsamples is 0.55+/-0.18dex and between pairs with and without interaction signs is 0.65+/-0.16dex. Together, our results suggest that (1) star formation enhancement in close major-merger pairs occurs mainly in S+S pairs after the first close encounter (indicated by interaction signs)^Mbecause the HI gas is compressed into star-forming molecular gas by the tidal torque; and (2) this effect is much weakened in the S+E pairs.