We report O K-edge and Cu L 23--edge X-ray-absorption near-edge-structure (XANES) spectra of oxycarbonase (Tl 0.8Cr 0.2)Sr 4Cu 2(CO 3)O 7 obtained using a bulk-sensitive X-ray fluorescence yield technique. The prominent features of the O 1s absorption edge in the (Tl 0.8Cr 0.2)Sr 4Cu 2(CO 3)O 7 compound are three distinct pre-edge peaks at 528.2, 529.3 and 530.5 eV, respectively. We ascribed these pre-edge peaks to excitations of O 1s electrons to predominant O 2p holes located in the CuO 2 planes, in the apical oxygen sites, and in the (Tl,Cr)-O planes, respectively. The average number of holes within the in-plane oxygen sites per CuO 2 sheet is approximately the same for both the (Tl 0.8Cr 0.2)Sr 4Cu 2(CO 3)O 7 and Tl 3(CrO 4)Sr 8Cu 4O 16 systems. Conversely, the average hole content in the apical oxygen sites decreases significantly in (Tl 0.8Cr 0.2)Sr 4Cu 2(CO 3)O 7 as compared to Tl 3(CrO 4)Sr 8Cu 4O 16. The reduction of the average hole concentration in the apical oxygen sites is accompanied by the enhanced superconductivity in (Tl 0.8Cr 0.2)Sr 4Cu 2(CO 3)O 7, indicating that the O 2p holes on the apical oxygen sites play an important role to control the T c. The behavior of the high-energy shoulders in the Cu L 23-edge absorption spectra coincides with that of the pre-edge peak at 528.2 eV in the O K-edge absorption spectra.