Muon-spin-relaxation study of the ground state of the two-dimensionalS=1kagoméantiferromagnet [2-(3-N-methyl-pyridium)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-1-oxyl 3-N-oxide]BF4

Zero- and longitudinal-field positive muon spin relaxation $\left({\mu }^{+}\mathrm{SR}\right)$ measurements were carried out from 300 K to 30 mK to study a ground state of $m-{\mathrm{MPYNN}\mathrm{\cdot }\mathrm{}\mathrm{BF}}_4$ which is known to be a two-dimensional kagomé antiferromagnet with $S=1\mathrm{}$ by ac-susceptibility measurements. An implanted muon is expected to make a hydrogen bonding state with ${\mathrm{F}}^{-}$ ions in the crystal. Muon-spin depolarization by a dynamically fluctuating component of an internal field was still observed at 30 mK. This fluctuating component is suggested to be caused by an intradimer ferromagnetic interaction of ${2J}_0{/k}_B=23.3\mathrm{}$ K between radicals. No clear long-range magnetic ordering of the dimer spins was observed down to 30 mK, suggesting that the ground state of $m-{\mathrm{MPYNN}\mathrm{\cdot }\mathrm{}\mathrm{BF}}_4$ was nonmagnetic.