Given the latest national regulations released on 24th March 2022 (n.24) and the end of the state of emergency:
 
starting from the 1st April 2022, the Green Pass (EU Covid Certificate) will not be necessary anymore

to visit museums, archaeological parks, exhibitions, archives, libraries and other cultural sites.

 NEW* starting from the 1st May 2022, wearing masks inside museums and other cultural sites is not mandatory anymore,

but it is still highly recommended.