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We present $\sim$0."3 (114 pc) resolution maps of [CI] $^{3}P_{1}$-$^{3}P_{0}$ (hereafter [CI] (1-0)) and $^{12}$CO (1-0) obtained toward Arp 220 with the Atacama Large Millimeter/submillimeter Array. The overall distribution of the [CI] (1-0) emission is consistent with the CO (1-0). While the [CI] (1-0) and CO (1-0) luminosities of the system follow the empirical linear relation for the unresolved ULIRG sample, we find a sublinear relation between [CI] (1-0) and CO (1-0) using the spatially-resolved data. We measure the [CI] (1-0)/CO (1-0) luminosity ratio per pixel in star-forming environments of Arp 220 and investigate its dependence on the CO (3-2)/CO (1-0) ratio ($R_{\rm CO}$). On average, the [CI] (1-0)/CO (1-0) luminosity ratio is almost constant up to $R_{\rm CO} \simeq 1$ and then increases with $R_{\rm CO}$. According to the radiative transfer analysis, a high CI/CO abundance ratio is required in regions with high [CI] (1-0)/CO (1-0) luminosity ratios and $R_{\rm CO} > 1$, suggesting that the CI/CO abundance ratio varies at $\sim$100 pc scale in Arp 220. The [CI] (1-0)/CO (1-0) luminosity ratio depends on multiple factors and may not be straightforward to interpret. We also find the high-velocity components traced by [CI] (1-0) in the western nucleus, likely associated with the molecular outflow. The [CI] (1-0)/CO (1-0) luminosity ratio in the putative outflow is 0.87 $\pm$ 0.28, which is four times higher than the average ratio of Arp 220. While there is a possibility that the [CI] (1-0) and CO (1-0) emission traces different components, we suggest that the high line ratios are likely because of elevated CI/CO abundance ratios based on our radiative transfer analysis. A CI-rich and CO-poor gas phase in outflows could be caused by the irradiation of the cosmic rays, the shock heating, and the intense radiation field.