We present a theoretical analysis of formation and kinetics of hot OH molecules in the upper atmosphere of Mars produced in reactions of thermal molecular hydrogen and energetic oxygen atoms. Two major sources of energetic O considered are the photochemical production, via dissociative recombination of O + 2 ions, and energizing collisions with fast atoms produced by the precipitating Solar Wind (SW) ions, mostly H + and He 2+ , and energetic neutral atoms (ENAs) originating in the charge-exchange collisions between the SW ions and atmospheric gases. Energizing collisions of O with atmospheric secondary hot atoms, induced by precipitating SW ions and ENAs, are also included in our consideration. The non-thermal reaction O + H 2 (v, j) → H + OH(v , j ) is described using recent quantum-mechanical state-to-state cross sections, which allow us to predict non-equilibrium distributions of excited rotational and vibrational states (v , j ) of OH and expected emission spectra. A fraction of produced translationally hot OH is sufficiently energetic to overcome Mars' gravitational potential and escape into space, contributing to the hot corona. We estimate the total escape flux from dayside of Mars for low solar activity conditions at about 5 × 10 22 s −1 , or about 0.1% of the total escape rate of atomic O and H. The described non-thermal OH production mechanism is general and expected to contribute to the evolution of atmospheres of the planets, satellites, and exoplanets with similar atmospheric compositions.