While researching a different question I came upon a blog post from an expat tax filing service that has an interesting statement.
The Italian Tax Authority requires expats to report all assets held outside the country, including savings accounts and property. If you hold assets outside of Italy, you must file a monitoring return form along with your Italian tax return, which is due September 30 each year. In addition, all investment or cash transfers in and out of the country must be reported. At the present time there is no plan to tax the assets or transfers, but failure to file the monitoring form may result in stiff penalties.
I cannot asses the validity of this as we are not yet residents nor have we needed to yet file an Italian tax return. The post is dated from 2012 and claims to have been updated in 2014. I do not know if I am allowed to post a link to the commercial site nor if I can supply the name of the tax service.