The first sunday of the month, as stated on the official page of the Italian Ministry of Culture, the entrance in the state museums and archeological parks is free.
It won’t be possible to make any reservation and priority of access will be exclusive only for people with disabilities and pregnant women.
For the Stanza Segreta di Michelangelo the online reservation remains mandatory, even during the days of free entry. But you won't have to pay any fare or fee of reservation.