Is it possible that $\ce{2 OH-}$ from water could react to form $\ce{H2O2}$?
I mean most autoionization forms $\ce{H3O+}$ and $\ce{OH-}$.
However I think it is possible that $\ce{H-}$ and $\ce{OH+}$ forms, though the amount formed of these 2 is small. This is from water acting as an acid and H+ acting as a base.