In this work, we present a comprehensive study on the hydrogen impurity depth profiles in InN films with polar c-plane and nonpolar a-plane surface orientations in relation to their structural and free-electron properties. We find that the as-grown nonpolar films exhibit generally higher bulk and near-surface H concentrations compared to the polar InN counterparts. The latter may be partly associated with a change in the growth mode from 2D to 3D and a decrease in the grain size. Thermal annealing leads to a reduction of H concentrations and the intrinsic H levels are influenced by the structural characteristics of the films. The factors allowing reduction of bulk H and free electron concentrations in a-plane films are discussed.