Time-resolved and steady state photoconductivity measurements were carried out on sexithiophene single crystals. We used a surface geometry, where two gold electrodes separated by 2 mm were deposited on the same side of the crystal. Time resolved measurements revealed fast and slow components. The first one, whose decay time is lower than 1 ns, is attributed to the conversion of charge transfer excitons into molecular excitons. The slow component behaves as a second order process, which is analyzed as bimolecular recombination of electrons and holes. It is preceded by an intermediate component that we tentatively ascribe to geminate recombination of the excitons. A similar analysis is used to rationalize the steady-state photocurrent. We find a quantum efficiency of around ${10}^{\ensuremath{-}4}.$ The coincidence between the photoluminescence and photocurrent action spectra, together with the low electric field applied over the crystal, suggest charge generation to occur via thermally activated splitting of molecular excitons. From the quantum efficiency at room temperature, the exciton binding energy is estimated to $0.50\ifmmode\pm\else\textpm\fi{}0.06\mathrm{eV}.$ This value is confirmed by the temperature dependent photocurrent.