compounds are two highly-frustrated magnets possessing a quasi-two-dimensional Kagomé bilayer of spin 3 2 / chromium ions with antiferromagnetic interactions. Their magnetic susceptibility was measured by local nuclear magnetic resonance and nonlocal (SQUID) techniques, and their low-temperature spin dynamics by muon spin resonance. Consistent with the theoretical picture drawn for geometrically frustrated systems, the Kagomé bilayer is shown here to exhibit: (i) short range spin-spin correlations down to a temperature much lower than the Curie-Weiss temperature, no conventional long-range transition occurring; (ii) a Curie contribution to the susceptibility from paramagnetic defects generated by spin vacancies; (iii) low-temperature spin fluctuations, at least down to 30 mK, which are a trademark of a dynamical ground state. These properties point to a spin-liquid ground state, possibly built on resonating valence bonds with unconfined spinons as the magnetic excitations.