A search for tribaryon states was performed at KEK-PS. We adopted the $^4$He($K^-_{stopped}, p)$ reaction to populate the states with strangeness -1, charge 0 and isospin 1. No significant narrow structure was observed in the mass region from 3000 to 3200 MeV/c^2 in an inclusive missing mass spectrum. The upper limit of the formation branching ratio was determined to be ($1sim3)times 10^{-4}$, ($0.7sim2)times 10^{-3}$ and ($2sim8) times 10^{-3}$/($stopped K^{-}$) with 95 % confidence level for narrow states with an assumed width of 0, 20 and 40 MeV/c^2, respectively.