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StoqMA captures the computational hardness of approximating the ground energy of local Hamiltonians that do not suffer the so-called sign problem. We provide a novel connection between StoqMA and distribution testing via reversible circuits. First, we prove that easy-witness StoqMA (viz. eStoqMA, a sub-class of StoqMA) is contained in MA. Easy witness is a generalization of a subset state such that the associated set’s membership can be efficiently verifiable, and all non-zero coordinates are not necessarily uniform. This sub-class eStoqMA contains StoqMA with perfect completeness (StoqMA₁), which further signifies a simplified proof for StoqMA₁ ⊆ MA [Bravyi et al., 2006; Bravyi and Terhal, 2010]. Second, by showing distinguishing reversible circuits with ancillary random bits is StoqMA-complete (as a comparison, distinguishing quantum circuits is QMA-complete [Janzing et al., 2005]), we construct soundness error reduction of StoqMA. Additionally, we show that both variants of StoqMA that without any ancillary random bit and with perfect soundness are contained in NP. Our results make a step towards collapsing the hierarchy MA ⊆ StoqMA ⊆ SBP [Bravyi et al., 2006], in which all classes are contained in AM and collapse to NP under derandomization assumptions.