Starburst merging galaxies are important in the history of galaxy evolution timeline. For this work, we have chosen the Antennae galaxy (NGC4039), which is one of the most famous starburst merging galaxies. We analyzed the CO (3–2) interferometric observations for the southern mosaic of the NGC 4039, together with the CO (2–1) data taken from Atacama Large Millimeter/Sub-millimeter Array (ALMA). Using the galactic CO luminosity to H2 mass conversion factor, we found molecular gas mass range in this galaxy to be (0.8–2.92) × 108 M☉. Line emissions at CO (2–1) and CO (3–2) were detected at selected regions in the nucleus of NGC 4039. The CO (3–2) / CO (2–1) ratio for this galaxy was calculated to be approximately 0.62. In addition, we found a significant correlation between the brightness temperature ratio and IR luminosity for this galaxy. We used a new model to interpret the rotation curve and found that the most important factor is related to gas mass distribution. The disturbance in the gas distribution may be caused by the merging process. We have also analyzed the spatially resolved star formation law in this galaxy up to 345 parsec. We found a breakdown of the Kennicutt–Schmidt law at this scale. The results are consistent with the previous findings that there is a possibility of sub-thermally excited widespread gas in the neighborhood of denser regions, which causes the flatter star formation law.