Zero-field muon spin-relaxation µSR measurements in 63Cu isotope enriched and natural YBa2Cu4O8 powders are presented. The µ+ relaxation rate is characterized by a sizeable enhancement as the temperature is lowered below the superconducting transition temperature Tc. The comparison of the asymmetry decay in the two samples reveals that the µ+ relaxation is driven by nuclear dipole interaction from 300 K down to 4.2 K. It is argued that the increase in the relaxation rate below Tc originates from a change either of the µ+ site or of the orientation of the electric-field gradient at the Cu nuclei, due to a modification in the charge distribution within CuO chains.