  We have carried out an experiment to search for a neutron-rich hypernucleus,
$^6_{\Lambda}$H, by the $^6$Li($\pi^-,K^+$) reaction at $p_{\pi^-}$ =1.2
GeV/$c$. The obtained missing mass spectrum with an estimated energy resolution
of 3.2 MeV (FWHM) showed no peak structure corresponding to the $^6_{\Lambda}$H
hypernucleus neither below nor above the $^4_{\Lambda}$H$+2n$ particle decay
threshold. An upper limit of the production cross section for the bound
$^6_{\Lambda}$H hypernucleus was estimated to be 1.2 nb/sr at 90% confidence
level.
