We report magnetization, heat capacity, Li7 nuclear magnetic resonance (NMR), and muon-spin rotation (μSR) measurements on the honeycomb 4d5 spin liquid candidate Li2RhO3. The magnetization in small magnetic fields provides evidence of the partial spin-freezing of a small fraction of Rh4+ moments at 6 K, whereas the Curie-Weiss behavior above 100 K suggests a pseudo-spin-1/2 paramagnet with a moment of about 2.2μB. The magnetic specific heat (Cm) exhibits no field dependence and demonstrates the absence of long-range magnetic order down to 0.35 K. Cm/T passes through a broad maximum at about 10 K and CmT2 at low temperatures. Measurements of the spin-lattice relaxation rate (1/T1) reveal a gapless slowing-down of spin fluctuations upon cooling with 1/T1∼T2.2. The results from NMR and μSR are consistent with a scenario in which a minority of Rh4+ moments are in a short-range correlated frozen state and coexist with a majority of moments in a liquid-like state that continue to fluctuate at low temperatures. © 2017 American Physical Society.