Understanding the functional status of people with Alzheimer Disease (AD), both in a single (ST) and cognitive dual task (DT) activities is essential for identifying signs of early-stage neurodegeneration. This study aims to compare the performance quality of several tasks using sensors embedded in an Android device, among people at different stages of Alzheimer and people without dementia. The secondary aim is to analyze the effect of cognitive task performance on mobility tasks. This is a cross-sectional study including 22 participants in the control group (CG), 18 in the group with mild AD and 22 in the group with moderate AD. They performed two mobility tests, under ST and DT conditions, which were registered using an Android device. Postural control was measured by medial-lateral and anterior-posterior displacements of the COM (MLDisp and APDisp, respectively) and gait, with the vertical and medial-lateral range of the COM (Vrange and MLrange). Further, the sit-to-stand (PStand) and turning and sit power (PTurnSit), the total time required to complete the test and the reaction time were measured. There were no differences between the two AD stages either for ST or DT in any of the variables (p > 0.05). Nevertheless, people at both stages showed significantly lower values of PStand and PTurnSit and larger Total time and Reaction time compared to CG (p < 0.05). Further, Vrange is also lower in CDR1G than in CG (p < 0.05). The DT had a significant deleterious effect on MLDisp in all groups (p < 0.05) and on APDisp only in moderate AD for DT. Our findings indicate that AD patients present impairments in some key functional abilities, such as gait, turning and sitting, sit to stand, and reaction time, both in mild and moderate AD. Nevertheless, an exclusively cognitive task only influences the postural control in people with AD.