  Altermagnets are a novel class of magnetic materials besides ferro- and
antiferromagnets, where the interplay of lattice and spin symmetries produces a
magnetic order that is staggered both in coordinate as well as momentum space.
The metallic rutile oxide RuO$_2$, long believed to be a textbook Pauli
paramagnet, recently emerged as a workhorse altermagnet when resonant X-ray and
neutron scattering studies reported nonzero magnetic moments and long-range
collinear order. While experiments on thin films seem consistent with
altermagnetic behavior, the origin and size of magnetic moments in RuO$_2$
still remain controversial. Here we show that RuO$_2$ is nonmagnetic,
regardless if as bulk or thin film. Employing muon spin spectroscopy as a
highly sensitive probe of local magnetic moments complemented by density
functional theory, we find at most $1.4 \times 10^{-4} $ $\mu_B$/Ru in bulk
RuO$_2$ and at most $7.5 \times 10^{-4}$ $\mu_B$/Ru in epitaxial films. In
their essence, these moments reflect the detection limit of our spectrometers
and are orders of magnitude smaller than previously reported neutron results,
i.e., the moments previously assumed to rationalize altermagnetic behavior. Our
own neutron diffraction measurements on RuO$_2$ single crystals identify
multiple scattering as a likely source for this discrepancy.
