  We investigate mixed-valence oxide Co$_3$O$_4$ using Co $2p3d$ resonant
inelastic X-ray scattering (RIXS). By setting resonant edges at Co$^{2+}$ and
Co$^{3+}$ ions, the $dd$ excitations on the two Co sites are probed
selectively, providing detailed information on the local electronic structure
of Co$_3$O$_4$. The $2p3d$ RIXS result reveals the $^4$T$_{2}$ excited state of
tetrahedral Co$^{2+}$ site at 0.5 eV beyond the discriminative power of optical
absorption spectroscopies. Additionally, the $^3$T$_{2g}$ excited stated at 1.3
eV is uniquely identified for the octahedral Co$^{3+}$ site. Guided by cluster
multiplet simulations, the ground-state character of the Co$^{2+}$ and
Co$^{3+}$ site is determined to be high-spin $^4$A$_{2}$(T$_d$) and low-spin
$^1$A$_{1g}$(O$_h$), respectively. This indicates that only the Co$^{2+}$ site
is magnetically active site at low-temperatures in Co$_3$O$_4$. The
ligand-to-metal charge transfer analysis suggests a formation of a strong
covalent bonding between Co and O ions at the Co$^{3+}$ site, while Co$^{2+}$
is rather ionic.
