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inquiries (or an investigation) in which both sides were heard
Explanation: Not the most elegant English, but that's the sense of it. The Ministry of Finance conducted one or more inquiries (or, collectively, an investigation), or the proceedings in question (the "accertamenti") were conducted at the offices of the Ministry of Finance, and each of the parties to the matter was given the opportunity to speak its piece (the "contraddittorio" part).
Hope this helps a bit,
Heathcliff United States Local time: 06:30 Native speaker of: English PRO pts in pair: 504