[ecesena]

As of today they did 275,468 tests: https://docs.google.com/spreadsheets/d/1xAyDSpzEp3n4iiu54_XL...

This is a post (sorry, in Italian) that describes the "strategy" adopted to test people, that of course varies by region. tl;dr: in regions like Lombardia (the most affected) they can almost only test people who really show severe signs, therefore the rate is around 38%.

https://www.ilpost.it/2020/03/20/tampone-test-coronavirus/

Official data is here: https://github.com/pcm-dpc/COVID-19, I just put it in a spreadsheet for easier consumption.

Edit: forgot a link