As a doctoral student, you should be insured in case of injuries at work, on the route to work, and while traveling for work.
If you are employed, you are likely covered by work-related insurance taken out by your employer. You can ask the HR department or administrative staff about this insurance.
If you are financed through a scholarship you are covered by insurance for doctoral students, provided by The Legal, Financial and Administrative Services Agency (Kammarkollegiet), a governmental agency mandated by the government to provide insurance for doctoral students. You are covered automatically and there are no special papers for you to sign.