In a Level 3 automated driving system, sometimes the driver may be asked to perform non-driving-related tasks because of a lack of engagement in the driving task. We conducted a driving simulator experiment to investigate the driver’s behavior when accepting the system’s request for manual driving under distracted condition by non-driving-related tasks. "Radio hearing task" and "text input task" were set for non-driving-related tasks; in addition, "no task" was set to a control condition. There was a tollgate where the limit of the automatic driving systems because of reached to the end of lane markers. The timing of starting brake was significantly later and maximum brake pedal force was larger in texting. Almost all drivers could resume driving from system, however there was one collision occurred in a texting condition. We suggest that the method for generating the request for deeply distracted driver should be considered.