ROME — Shortly after Rome’s municipal elections last year, Massimo Carminati, a reputed mobster better known as The Pirate or The Blind One for having lost an eye in a shootout years ago, passed along some advice about how to deal with City Hall’s fresh stock of administrators and politicians.

“You tell them, now that we’ve done this one thing, what are your next plans?” he told a contact in June 2013. “What do you need? What can I do? How can I make money?

“You need me to dig ditches? Erect billboards?” he continued, gathering steam as his language turned coarse. “Fine, I’ll do it, because if I then find out that someone else did it — do you understand? — then it becomes something unpleasant.”

That conversation and scores of others, intercepted by investigators, have added a splash of color to an otherwise dark two-year inquiry that resulted last week in the arrest of Mr. Carminati and 36 others accused of bullying their way into dozens of lucrative public tenders in the Italian capital.