The quasi-one-dimensional hollandite vanadate K₂V₈O₁₆is believedtohavea spin-singlet-like transitionat ≈ 170 K.Weinvestigateda polycrystalline sampleof K₂V₈O₁₆ using zero-field μSR.Paramagnetic electronic fluctuations, manifested as a relaxation of the muon polarization function, exist at all temperatures. There are only smooth and slight changes in the relaxation rate as the temperature of the sample is decreased from 200 K. Below about 10 K, there is a significant increase in the relaxation rate, implying a slow-down of the paramagnetic fluctuations.