Which kind of criminal record certificate is required for citizenship in Italy?

I am a UK citizen married to an Italian living in Italy. I have had permanent residency for 5 years and would now like to apply for Citizenship in Italy, due to the whole Brexit!
As far as the criminal record check goes, I already have a DBS certificate, (disclosure and baring service) is this enough or do I need a different kind of criminal record certificate? Please help!