The temperature dependent current-voltage (J-V) characteristics of highly-oriented cobalt phthalocyanine films (rocking-curve width=0.11°) deposited on (001) LaAlO₃ substrates are investigated. In the temperature range 300-100 K, charge transport is governed by bulk-limited processes with a bias dependent crossover from Ohmic (J ~ V) to trap-free space-charge-limited conduction (J ~ V²). The mobility (µ) at 300 K has a value of ~ 7 cm² V^-1 s^-1 and obeys Arrhenius-type    (ln µ ~ 1/T) behavior. However, at temperatures < 100 K, the charge transport is electrode-limited, which undergoes a bias dependent transition from Schottky      (ln J ~ V^1/2) to multistep-tunneling (conductivity varying exponentially on the inverse of the square-root of electric field).