  In this paper, we shall treat the Schr\"odinger forms with non-local
perturbations. We first extend the definitions of subcriticality, criticality
and supercriticality for the Schr\"odinger forms by Takeda in [IJM, 2015] to
the non-local cases in the context of quasi-regular Dirichlet forms. Then we
prove an analytic characterization of these definitions via the bottom of the
spectrum set.
