In this paper, we propose line current sensor fault detection for AC drives. The method is based on the measured currents and the features are extracted either in the natural reference frame or in the transformed Park synchronous rotating frame. The features are the first four statistical moments or the Kullback Leibler Divergence (KLD) of the Probability Density Functions (PDF). For offset fault, we show that if the offset is higher than 3% of the current amplitude, the mean value is the most relevant value among the first four statistical moments that leads to good detection performances (low probability of false alarm and low probability of miss detection). But for incipient faults (offset ranging from 1 to 2%), even the projection in the transformed Park reference frame cannot improve the fault detection. For these cases, we show that the fault information can be retrieved using the PDF and the KLD. This is confirmed by the results showing that the fault is detected with 100% probability of detection.