We present new high-resolution 12CO J = 1–0, J = 2–1, and 13CO J = 1–0 maps of the early stage merger Arp 240 (NGC 5257/8) obtained with the Atacama Large Millimeter/submillimeter Array (ALMA). Simulations in the literature suggest that the merger has just completed its first passage; however, we find that this system has a lower global gas fraction but a higher star formation efficiency (SFE) compared to typical close galaxy pairs, which suggests that this system may already be in an advanced merger stage. We combine the ALMA data with 12CO J = 3–2 observations from the Submillimeter Array and carry out RADEX modelling on several different regions. Both, the RADEX modelling and a local thermal equilibrium (LTE) analysis show that the regions are most likely to have a CO-to-H2 conversion factor αCO close to or perhaps even smaller than the typical value for (ultra)luminous infrared galaxies. Using 33-GHz data from the Very Large Array to measure the star formation rate, we find that most star-forming regions have molecular gas depletion times of less than 100 Myr. We calculated the SFE per free-fall time for different regions and find some regions appear to have values greater than 100 per cent. We find these regions generally show evidence for young massive clusters (YMCs). After exploring various factors, we argue that this is mainly due to the fact that radio continuum emission in those regions is dominated by that from YMCs, which results in an overestimate of the SFE per free-fall time.