Thanks to the agreement between the University of Trento and the local Provincial Company for Health Services (APSS), if you are a PhD student resident in Italy (but not in the Province of Trento) and you are registered in the National Health Service (SSN) you can go to a primary care doctor for a visit in Trentino, even for free, without the need to be deleted from the registration with your health practitioner (ASL) in the place of residence.
To qualify for basic medical assistance, your enrollment must be active for the current academic year.
All details are available at Infostudenti (in Italian only).