[en] We have searched for rare and forbidden decays of the η^' meson in hadronic events at the CLEO II detector. The search is conducted on 4.80 fb^-1 of e⁺e^- collisions at 10.6 GeV center-of-mass energy at the Cornell Electron Storage Ring. We find no signals, and set 90% confidence level upper limits of their branching fractions: B(η^'→e⁺e^- η)<2.4x10^-3 , B(η^'→e⁺e^- π⁰)<1.4x10^-3 , B(η^'→e⁺e^- γ)<0.9x10^-3 , and B(η^'→eμ)<4 .7x10^-4 . We also fit the matrix element of the η^'→π⁺π^-η Dalitz plot with the parametrization |M|²=A|1+αy|² , where y is a linear function of the kinetic energy of the η , and find Re(α)=-0.021±0.025 . (c) 1999 The American Physical Society