We report on measurements of nonresonant inelastic x-ray scattering (NIXS) to unravel the effective symmetry of Cu $3d$ orbitals in the ground state of CuO. A clear feature of energy loss at about 2 eV exists in the NIXS spectrum, arising from $dd$ excitations; the intensities of these excitations display a pronounced anisotropy. The comparison between the measured angular distributions of scattering and those from theoretical predictions by the tesseral harmonics indicates that, in terms of a hole picture, the lowest-energy $dd$ excitation is the orbital transition ${x}^{2}\ensuremath{-}{y}^{2}$ $\ensuremath{\rightarrow}$ $xy$. In addition, the transition ${x}^{2}\ensuremath{-}{y}^{2}$ $\ensuremath{\rightarrow}$ $3{z}^{2}\ensuremath{-}{r}^{2}$ has an energy higher than ${x}^{2}\ensuremath{-}{y}^{2}$ $\ensuremath{\rightarrow}$ $yz/zx$, in contrast to a previous interpretation. Our results imply a large Jahn-Teller-like splitting between ${x}^{2}\ensuremath{-}{y}^{2}$ and $3{z}^{2}\ensuremath{-}{r}^{2}$ orbitals. The theory assuming a ${C}_{4h}$ symmetry explains the angular dependence of the NIXS spectra fairly well, implying that this symmetry is a reasonable approximation. This demonstrates that NIXS can provide important information for modeling of the electronic structure of $d$ ions embedded in a complicated crystal field.