The metallic ruthenium perovskites ACu₃Ru₄O₁₂ with A Ca, Pr,Nd were investigated by zero field (ZF) and weak transverse field (TF) muon spin rotation/relaxation (μSR) spectroscopy. The ZF spectra for CaCu₃Ru₄O₁₂ show pure static Gaussian Kubo-Toyabe relaxation arising from the interaction between the muon spin and the nuclear moments of the Cu ions. This confirms that no atomic magnetic moment exists. A sudden increase of the lattice parameter a when heating above ~150 K had previously been detected by neutron diffraction. The root mean square field at the muon site B_rms was found to be 0.15 mT independent of temperature, in particular around 150 K. Also, no change of spectral parameters is seen in the weak TF data in that temperature range. Those findings imply that the structural change around 150 K takes place without noticeably shifting atomic positions. The spectra for PrCu₃Ru₄O₁₂ and NdCu₃Ru₄O₁₂ are dominated by the interaction with the dynamic rare earth moments. The analysis requires the use of the electron-nuclear double relaxation formalism. The electronic part shows simple exponential relaxation typical for a paramagnet. It features, with reducing the temperature a steep increase of paramagnetic relaxation rate as is characteristic for an approach to a magnetic spin freezing transition from above. That result suggests that the magnetic ground states of PrCu₃Ru₄O₁₂ and NdCu₃Ru₄O₁₂ are spin frozen states, although bulk magnetic data give no direct evidence in that direction.