  Recently, rutile RuO$_2$ has raised interest for its itinerant
antiferromagnetism, crystal Hall effect, and strain-induced superconductivity.
Understanding and manipulating these properties demands resolving the
electronic structure and the relative roles of the rutile crystal field and
$4d$ spin-orbit coupling (SOC). Here, we use O-K and Ru $M_3$ x-ray absorption
(XAS) and Ru $M_3$ resonant inelastic x-ray scattering (RIXS) to disentangle
the contributions of crystal field, SOC, and electronic correlations in
RuO$_2$. The locally orthorhombic site symmetry of the Ru ions introduces
significant crystal field contributions beyond the approximate octahedral
coordination yielding a crystal field energy scale of $\Delta(t_{2g})\approx 1$
eV breaking the degeneracy of the $t_{2g}$ orbitals. This splitting exceeds the
Ru SOC ($\approx160$ meV) suggesting a more subtle role of SOC, primarily
through the modification of itinerant (rather than local) $4d$ electronic
states, ultimately highlighting the importance of the local symmetry in
RuO$_2$. Remarkably, our analysis can be extended to other members of the
rutile family, thus advancing the comprehension of the interplay among crystal
field symmetry, electron correlations, and SOC in transition metal compounds
with the rutile structure.
