We have studied the electrical properties of a fluorene-containing copolymer which is currently being developed for state-of-the-art blue polymer LEDs. This copolymer is made up of three functional groups which are nominally the hole-conducting, electron conducting and emissive regions. Using a combination of current/voltage, time-of-flight and dark injection transient versus temperature measurements, the injection and transport properties of the material have been investigated. Hole injection from polystyrene sulphonate doped polyethylenedioxythiophene (PEDOT:PSS) into the polymer is found to be consistent with an ohmic contact. Hole transport within the fluorene copolymer is found to possess a mobility that is two orders of magnitude lower than that for previously studied polymers containing the copolymer constituents. Using the equations for trap-free space-charge limited current, predicted J/V characteristics have been obtained from the mobility values derived using the time-of-flight technique. We discuss both the reduced hole mobility of the copolymer, and the discrepancies between the measured and predicted J/V characteristics, in terms of variations in both the trap and transport site densities and their energetic and spatial distributions.