[en] Photoionization of H₂(¹Σsub(g)⁺) in a vibrational upsilon'' and rotational NU'' state into H₂⁺(²Σsub(g)⁺) in a vibrational upsilon' and rotational NU' state is studied theoretically. Parallel expressions are obtained for H₂⁺ in a specific upsilon' state and for H₂⁺ in a rotational fine level upsilon'NU'. Asymmetry parameters β, β(upsilon') and β(upsilon'NU') which are expressed in terms of Racah and Clebsch-Gordan coefficients and electronic transition moments, can be reduced approximately to 2 for linearly polarized light and to -1 for unpolarized light. Using single-center electronic wave functions and including partial waves l = 1, 3, and 5, σ(upsilon') and β(upsilon') are computed as a function of upsilon' at 584A. The computed σ(upsilon') divided by the Frank-Gondon overlap, in agreement with experimental results, increases monotonically with upsilon'; σsub(T) and β are computed in the incident photon energy range of 600-400 A and the results compare favorably with previous calculations. (author)