The magnetic ground state of single crystalline RuO_{2} was investigated by the muon spin rotation and relaxation (μSR) experiment. The spin precession signal due to the spontaneous internal magnetic field B_{loc}, which is expected in the magnetically ordered phase, was not observed in the temperature range 5-400 K. Muon sites were evaluated by first-principles calculations using dilute hydrogen simulating muon as pseudohydrogen, and B_{loc} was simulated for the antiferromagnetic structures with a Ru magnetic moment |m_{Ru}|≈0.05μ_{B} suggested from diffraction experiments. As a result, the possibility was ruled out that muons are localized at sites where B_{loc} accidentally cancels. Conversely, assuming that the slow relaxation observed in μSR spectra was part of the precession signal, the upper limit for the magnitude of |m_{Ru}| was estimated to be 4.8(2)×10^{-4}μ_{B}, which is significantly less than 0.05μ_{B}. These results indicate that the antiferromagnetic order, as reported, is unlikely to exist in the bulk crystal.