  The magnetic state of the single-component molecular compound,
[Cu(tmdt)$_{2}$], is investigated by means of $^{1}$H-NMR. An abrupt spectral
broadening below 13 K and a sharp peak in nuclear spin-lattice relaxation rate,
$T_{1}^{-1}$, at 13 K are observed as clear manifestations of a second-order
antiferromagnetic transition, which is consistent with the previously reported
magnetic susceptibility and EPR measurement. The ordered moment is estimated at
$0.22-0.45$ ${\mu}_{\rm B}$/molecule. The temperature-dependence of
$T_{1}^{-1}$ above the transition temperature indicates one-dimensional spin
dynamics and supports that the spins are on the central part of the molecule
differently from other isostructural compounds.
