We study excitons in crystalline thin films of the archetype organic molecular compound 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA) by measuring the photocurrent response under small electric fields (< 10(4) V/cm). Photocurrent data reveal the existence of a response tail at energies from E = 1.99 to 2.10 eV above the PTCDA highest occupied molecular orbital, corresponding to a previously identified (Paper I) self-trapped exciton located at E = 2.11 +/- 0.04 eV. The diffusion length of this self-trapped state is L(D) = 225 +/- 15 nm, compared to L(D) = 88 +/- 6 nm for excitons generated between E = 3.27 and 2.36 eV. Fits to absorption data also indicate strong mixing between this self-trapped state and the E = 2.23 eV charge transfer exciton, Exciton diffusion lengths are extracted using a simple model of photocurrent generation in low electric fields, which includes the effects of exciton diffusion, dissociation at the organic/electrode interfaces, and subsequent carrier transport. The data reconfirm that PTCDA is preferentially hole conducting material which is lightly ''p-type'' at equilibrium. This paper is the second in a two part series investigating excitons in PTCDA thin films.