A differential rotation of the inner core with respect to the mantle has been recently detected from the variations in time of the inner core anisotropy symmetry axis. This detection relies on the assumption that the anisotropy axis is tilted with respect to the rotation axis. We show that such a tilt cannot be reliably detected with the presently available data. In addition, we observe an apparent correlation between the differential travel time residuals of the core phases used to infer inner core rotation, and the magnitude of the events. This correlation, which could result from the analysis method of the data and from their varying frequency content, may partly bias the observations. Although these results do not rule out the possibility of an inner core differential rotation, they question whether it has actually been detected.¿ 1997 American Geophysical Union