Who should do the fall paper work

The nurse who had been working on the floor where the fall occured had already given report and was punched out already. The night nurse was getting report from another nurse. I was trying finish my charting and still had to give report. It was about 5 minutes left of my shift. The aid called the nurses station and wanted the nurse to come down because a resident had fallen. Since the night nurse was still getting report I went down and assessed her and she didn't have any apparent injury. I charted in the chart and had the aid fill out a witness statement. I did that to help the night nurse out. She wanted me to fill out all the paper work. I still had to give her report and finish my charting. We are not to have any overtime. Do you think I was wrong to ask the night nurse to do the rest of the paper work.