The dissociation pathways of HeH+ have been investigated below the first ionization continuum by photoabsorption at 32 nm, using fragment momentum imaging in a crossed-beams experiment at the free-electron laser in Hamburg (FLASH). Investigations were done both for ions with several vibrational levels excited in the ion source and for ions vibrationally cooled in an electrostatic ion trap prior to the irradiation. The product channels He+(1s)+H(nl) and He(1snl)+H+ were separated and the He(1snl)+H+ channel was particularly studied by coincidence detection of the He and H+ fragments on two separate fragment detectors. At 32 nm excitation, the branching ratio between the product channels was found to be sigmaHe++H/sigmaHe+H+=0.96±0.11 for vibrationally hot and 1.70±0.48 for vibrationally cold ions. The spectra of kinetic energy releases for both channels revealed that photodissociation at 32 nm leads to high Rydberg states (n≳3-4) of the emerging atomic fragments irrespective of the initial vibrational excitation of HeH+. The fragment angular distributions showed that dissociation into the He+H+ channel mostly (~70%) proceeds through 1Pi states, while for the He++H channel 1Sigma and 1Pi states are of about equal importance.