Electronic quenching of OH A ²Σ⁺ by molecular hydrogen is known to be an efficient process. The process proceeds through conical intersection regions which produce nonreactive (OH X ²Π + H₂) and reactive products (H₂O + H). This work describes investigations into the nonreactive quenching channel. The experiments utilize a pump-probe scheme to determine the OH X ²Π population distribution following collisional quenching in a pulsed supersonic expansion. The pump laser excites OH A ²Σ⁺ (v′=0, N′=0), which has a significantly reduced lifetime due to quenching by H₂. The probe laser monitors OH X ²Π (v″, N″) populations via laser-induced fluorescence on various A-X transitions under single-collision conditions. The experiments reveal a high degree of rotational excitation (N″) of the quenched OH X ²Π products observed in v″=0, 1 and 2 as well as a pronounced propensity for quenching into the Π(A') Λ-doublet level. The majority of the observed quenched OH X ²Π population lies in the lowest vibrational state (v″=0). The experimental results will be discussed with respect to multi-reference, configuration-interaction calculations aimed at exploring the topology of the relevant potential energy surfaces.