The nature of a spin-liquid ground state of a quantum kagome antiferromagnet remains elusive despite numerous theoretical studies in recent years. Therefore, in-depth experimental investigations of novel promising spin-liquid candidates are highly desired. We propose a muSR study of the recently discovered ZnCu3(OH)6SO4 that is believed to exhibit a unique two different gapless spin-liquid regimes. We believe that muSR could provide a valuable microscopic probe to inspect the re-entrance of the spin-liquid ground state and to address the nature of both gapless states.