We study the transition between positive and negative organic magnetoresistance (OMAR) in tris-(8 hydroxyquinoline) aluminium (Alq3), in order to identify the elementary mechanisms governing this phenomenon. We show how the sign of OMAR changes as function of the applied voltage and temperature. The transition from negative to positive magnetoresistance (MR) is found to be accompanied by an increase in slope of log (I) versus log (V). ac admittance measurements show this transition coincides with the onset of minority charge (hole) injection in the device. All these observations are consistent with two simultaneous contributions with opposite sign of MR, which may be assigned to holes and electrons having different magnetic field responses.