Taking over the manual control of a car after automated driving (AD) is a key issue for future road safety. However, performance to resume this manual control may be dependant on the driver's level of engagement in driving during AD. Indeed, according to the level of automation (from L2 to L3 of the SAE), drivers will be in charge of monitoring the driving situation, or will be allowed to perform non-driving-related tasks and thus to be fully disengaged from the driving task. In this context, the present study aims to investigate the influence of the driver's level of engagement/disengagement during AD on takeover performance using a driving simulator. Four levels of engagement/disengagement were studied: (C1) being engaged in driving situation monitoring without TakeOver Request (TOR) to resume manual control, (C2) being engaged in driving situation monitoring with a TOR to resume manual control, (C3) being disengaged from driving monitoring by performing a cognitively demanding secondary task with a TOR to resume manual control, and (C4) being disengaged from the driving monitoring in a relaxed position situation with eyes closed and with a TOR to resume manual control. Forty participants performed 16 critical takeover scenarios involving different critical takeover situations. Drivers' reaction times and collision risks were measured to assess their takeover performances and to investigate the safety of automation levels 2 and 3. Driving situation monitoring with a TOR (C2) induced the shortest reaction times and a lower number of collisions. For the relaxed posture (C4), drivers took a longer time to react than in the other three conditions. Driving situation monitoring without TOR (C1) had the highest number of collisions. This suggests that engagement in driving is not always effective and efficient without TOR. Moreover, being in a relaxed position during automated driving decreases takeover performance.