The theory of the photodissociation of diatomic molecules to open-shell atoms is applied to the near-threshold dissociation of CH⁺. Close-coupled calculations for the photodissociation cross-section and various anisotropy parameters exhibit a wealth of structure in conformity with our previous theoretical predictions that non-adiabatic interactions between molecular states, approaching the same atomic term limit, lead to the emergence of resonance features in the spectra. Some of these features are associated with Feshbach and shape resonances on states that carry no oscillator strength in zeroth order. The particular quantities evaluated are the total photodissociation cross-sections for the production of individual C⁺(²P_3/2,1/2) states from selected initial CH⁺ levels and the fragment angular distribution, orientation and alignment. Certain resonances are more pronounced in the anisotropy parameters than in the total cross-section, indicating further that their measurement would aid in the experimental assignment of resonances in photodissociation. The calculations provide a qualitative understanding of the complexity of the available experimental data for the photodissociation of CH⁺.