Yes, it is reasonable to request this and they may get it. That's because of two reasons:1) First and foremost, if you are injured, they only have to pay compensation to the extent that your injuries or conditions were caused by the accident. They do not need to pay for anything pre-existing or caused by prior injuries or accidents; therefore, they need to know about your medical background.2) Sometimes a medical condition can contribute to the accident (e.g. if you had diabetes and weren't taking proper care of yourself, that could cause you to lose control while driving) and so could bear on fault or liability.