We present the new single dish CO ( 3–2 ) emission data obtained toward 19 early stage and 7 late stage nearby merging galaxies using the Atacama Submillimeter Telescope Experiment ( ASTE ) . Combining with the single dish and interferometric data of galaxies observed in previous studies , we investigate the relation between the CO ( 3–2 ) luminosity ( L ^ { \prime } _ { CO ( 3 - 2 ) } ) and the far Infrared luminosity ( L _ { FIR } ) in a sample of 29 early stage and 31 late stage merging galaxies , and 28 nearby isolated spiral galaxies . We find that normal isolated spiral galaxies and merging galaxies have different slopes ( \alpha ) in the \log L ^ { \prime } _ { CO ( 3 - 2 ) } - \log L _ { FIR } plane ( \alpha \sim 0.79 for spirals and \sim 1.12 for mergers ) . The large slope ( \alpha > 1 ) for merging galaxies can be interpreted as an evidence for increasing Star Formation Efficiency ( SFE= L _ { FIR } / L ^ { \prime } _ { CO ( 3 - 2 ) } ) as a function of L _ { FIR } . Comparing our results with sub-kpc scale local star formation and global star-burst activity in the high-z Universe , we find deviations from the linear relationship in the \log L ^ { \prime } _ { CO ( 3 - 2 ) } - \log L _ { FIR } plane for the late stage mergers and high-z star forming galaxies . Finally , we find that the average SFE gradually increases from isolated galaxies , merging galaxies , and to high-z submillimeter galaxies / quasi-stellar objects ( SMGs/QSOs ) . By comparing our findings with the results from numerical simulations , we suggest ; ( 1 ) inefficient star-bursts triggered by disk-wide dense clumps occur in the early stage of interaction and ( 2 ) efficient star-bursts triggered by central concentration of gas occur in the final stage . A systematic high spatial resolution survey of diffuse and dense gas tracers is a key to confirm this scenario .