Here's all you need to know:

Under Italian Law (1939 and 1976) Fossil finds also count as cultural artefacts. In most regions and provinces of Italy, the scientific responsibility thereof lies with their respective natural museums, and the palaeontologists in their employ.

In the Autonomous Province of Bolzano, the following regulations apply:

Fossil mining is prohibited throughout the Province!
Collectors must inform themselves on-site regarding compliance with legislation. Violations are subject to hefty penalties.
Special permits for collecting minerals in the nature parks, or collecting fossils throughout the Province, are issued exclusively for scientific purposes.
Cultural artefacts are State property
Archaeological and cultural artefacts are, under Italian law, the property of the State. If any person chances upon a find, they do not become the owner; if a person has made a find of paleontological importance, Italian law stipulates that they must hand it over to the relevant legal representative of the State within 48 hours (Heritage Office, Police, Forestry Commission, Carabinieri etc.). After having undergone examination, finds are transferred to a museum depot, where the finder can view them at any time, provided their personal details were recorded at the time they were handed over.

If a fossil or stone is found that may or may not be of scientific/paleontological interest, the standard procedure is as follows:

-Record the finder’s personal details.
-Keep the item or take a photo of it (NB! Scale must be visible!).
-Forward the photo to the regional palaeontology officer.
-If, after examination, the find is determined not to be of scientific interest, the finder can, in theory, keep it, but under the understanding that the owner of the property remains, nevertheless, the State or the Autonomous Province of Bolzano.