We present CO(3-2) interferometric observations of the central region of the Seyfert 2 galaxy NGC1068 using the Submillimeter Array, together with CO(1-0) data taken with the Owens Valley Radio Observatory Millimeter Array. Both the CO(3-2) and CO(1-0) emission lines are mainly distributed within 5arcsec of the nucleus and along the spiral arms, but the intensity distributions show differences: the CO(3-2) map peaks in the nucleus, while the CO(1-0) emission is mainly located along the spiral arms. The CO(3-2)/CO(1-0) ratio is about 3.1 in the nucleus, which is four times as large as the average line ratio in the spiral arms, suggesting that the molecular gas there must be affected by the radiation arising from the active galactic nucleus. On the other hand, the line ratios in the spiral arms vary over a wide range from 0.24 to 2.34 with an average value around 0.75, which is similar to the line ratios of star formation regions, indicating that the molecular gas is affected by star formation. Besides, we see a tight correlation between CO(3-2)/(1-0) ratios in the spiral arms and star formation rate surface densities derived from Spitzer 8 μm dust flux densities. We also compare the CO(3-2)/(1-0) ratio and the star formation rate at different positions within the spiral arms; both are found to decrease as the radius from the nucleus increases.