A muon-spin relaxation (muSR) investigation is presented for the molecular superconductor kappa-(BEDT-TTF)2Cu[N(CN)2Br]. Evidence is found for low-temperature phase-separation, with only a fraction of the sample showing a superconducting signal, even for slow cooling. Rapid cooling reduces the superconducting fraction still further. For the superconducting phase, the in-plane penetration depth is measured to be lambda_{parallel} = 0.47(1) mu m and evidence is seen for a vortex decoupling transition in applied fields above 40 mT. The magnetic fluctuations in the normal state produce Korringa behavior of the muon spin relaxation rate below 100 K, a precipitous drop in relaxation rate is seen at higher temperatures and an enhanced local spin susceptibility occurs just above T_c.
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