The D0 collaboration has performed a study of spin correlation in $t\overline{t}$ production for the process $t\overline{t}\ensuremath{\rightarrow}{\mathrm{bW}}^{+}\overline{b}{W}^{\ensuremath{-}}$, where the $W$ bosons decay to $e\ensuremath{\nu}$ or $\ensuremath{\mu}\ensuremath{\nu}$. A sample of six events was collected during an exposure of the D0 detector to an integrated luminosity of approximately $125{\mathrm{pb}}^{\ensuremath{-}1}$ of $\sqrt{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\mathrm{TeV}$ $p\overline{p}$ collisions. The standard model (SM) predicts that the short lifetime of the top quark ensures the transmission of any spin information at production to the $t\overline{t}$ decay products. The degree of spin correlation is characterized by a correlation coefficient $\ensuremath{\kappa}$. We find that $\ensuremath{\kappa}>\ensuremath{-}0.25$ at the $68%$ confidence level, in agreement with the SM prediction of $\ensuremath{\kappa}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.88$.