I live in Lombardy, and I can assure you that the conditions to meet in order to get tested are the same. Me and my three flatmates had 37-39 °C for some days, including a very bad cough. We called the emergency number, and they said that they could test us only in case of prolonged temperature and/or respiratory problems. This happened like 2-3 weeks ago, and considering the current state of the national health service, I don't think requirements became lesse strict