Using muon-spin resonance, we examine the organometallic hybrid compound Cu(1,3-benzenedicarboxylate) [Cu(1,3-bdc)], which has structurally perfect spin-½ copper kagome planes separated by pure organic linkers. This compound has antiferromagnetic interactions with Curie-Weiss temperature of -33 K. We found slowing down of spin fluctuations starting at T=1.8 K and that the state at T→0 is quasistatic with no long-range order and extremely slow spin fluctuations at a rate of 3.6 μs^-1. This indicates that Cu(1,3-bdc) behaves as expected from a kagome magnet and could serve as a model kagome compound.