Even if they can't test everyone who dies for Covid-19, I'm sure Italy is recording the total number of deaths. It should be possible to determine how much the total death rate increased each week or month relative to the average death rate over the past few years.

EDIT: I found a non-paywall version of the article on MSN and that's essentially what they're reporting. "Nowhere in Italy has been harder hit than Bergamo, a city of about 120,000 people. In March 2019, 125 people died in the city. This March, 553 people died."

https://www.msn.com/en-us/news/world/italys-coronavirus-deat...