Numerous experimental studies, mostly based on the time-of flight (TOF) technique, showed that the conductivity in organic crystals can be analysed in terms of (trap-controlled) band transport. However, recent comparative studies of TOF signals and space charge limited currents (SCLCs) in tetracene crystals revealed a striking difference in carrier mobilities estimated from TOF current transients and from SCLC curves. The analysis of the SCLC curves yielded the mobilities wildly varying within 6 orders of magnitude. Therefore, it is not always clear whether the measured current-voltage (IV) device characteristics are controlled by charge injection or by transport in the bulk. In this work, we formulate a model of dopant-assisted carrier injection across a metal/organics interface and use this model for the analysis of IV curves measured on a tetracene and perylene crystal. The model suggests the occurrence of an energetically disordered layer at the surface of an organic crystal. This might be either an amorphous phase of the same material or a crystalline layer with a high density of defects and/or impurities. Since, at variance with bulk properties, the surface of an organic crystal is poorly controlled and can be strongly modified upon the contact deposition, the model of injection-controlled IV characteristics can explain the striking difference between the TOF mobility and the apparent ‘SCLC mobility’ measured in tetracene crystals. In order to give more credence to the role of surface defects states in the dark charge transport, we compare IV characteristics measured on sandwich and coplanar structures. In the latter structure, surface states show a major contribution to the conductivity.