The cubic double perovskite Ba2YIrO6 has been investigated by the local probe techniques nuclear magnetic resonance (Y-89 NMR) and muon spin rotation (mu SR). Both methods confirm the absence of magnetic long-range order in this compound but find evidence for diluted localized paramagnetic moments. NMRspin-lattice relaxation rate T-1(-1) measurements suggest a slowing down of localized spin moments at low temperatures. An increase of the mu SR spin-lattice relaxation rate lambda confirms the presence of weak magnetism in Ba2YIrO6. However, these findings cannot be explained by the recently suggested excitonic type of magnetism. Instead, they point towards tiny amounts of localized paramagnetic spin centers leading to this magnetic response on the background of a simple nonmagnetic ground state of the 5d(4) (J = 0) electronic configuration of Ir5+.