Effects of electronic nonlocality in density functional theory study of structural and energetic properties of a pseudocubic CH3NH3PbI3 are investigated by considering coherent rotation around C-N axis of a CH3NH3 cation. A number of truly non-local and semi-local exchange correlation density functionals are examined by comparing calculated structural parameters with experimental results. The vdW-DF-cx which takes into account the non-local van der Waals correlation and consistent exchange shows the best overall performance for density functional theory study of this system. Remarkable distinctions between results from vdW-DF-cx and those from PBEsol exchange correlation functionals are observed and indicate the need of including the non-local interaction in the study of this system, especially its dynamical properties. The obtained rotational barriers are 18.56 meV/formula and 27.71 meV/formula which correspond to rotational frequencies of 3.71 THz and 2.60 THz for vdW-DF-cx and PBEsol calculations, respectively. Interestingly, the maximally localised Wannier function analysis shows the hydrogen bonding assisted covalent character of two iodide anions at a moderate rotational angle which can lead to I2 formation and then material degradation.