  We introduce an analogue to Kato's Criterion regarding the inviscid
convergence of stochastic Navier-Stokes flows to the strong solution of the
deterministic Euler equation. Our assumptions cover additive, multiplicative
and transport type noise models. This is achieved firstly for the typical noise
scaling of $\nu^\frac{1}{2}$, before considering a new parameter which
approaches zero with viscosity but at a potentially different rate. We
determine the implications of this for our criterion and clarify a sense in
which the scaling by $\nu^\frac{1}{2}$ is optimal. To enable the analysis we
prove the existence of probabilistically weak, analytically weak solutions to a
general stochastic Navier-Stokes Equation on a bounded domain with no-slip
boundary condition in three spatial dimensions, as well as the existence and
uniqueness of probabilistically strong, analytically weak solutions in two
dimensions. The criterion applies for these solutions in both two and three
dimensions, with some technical simplifications in the 2D case.
