Compared with wakefulness, neuronal activity during nonrapid eye movement (NREM) sleep is characterized by a decreased ability to integrate information, but also by the reemergence of task-related information patterns. To investigate the mechanisms underlying these seemingly opposing phenomena, we measured directed information flow by computing transfer entropy between neuronal spiking activity in three cortical regions and the hippocampus of rats across brain states. State-dependent information flow was jointly determined by the anatomical distance between neurons and by their functional specialization. We distinguished two regimes, operating at short and long time scales, respectively. From wakefulness to NREM sleep, transfer entropy at short time scales increased for interareal connections between neurons showing behavioral task correlates. Conversely, transfer entropy at long time scales became stronger between nontask modulated neurons and weaker between task-modulated neurons. These results may explain how, during NREM sleep, a global interareal disconnection is compatible with highly specific task-related information transfer.