No, that type of background check results will not be reported to any immigration agency. Put your mind at ease. Which which Italian Consulate requested this type of background checks? San Francisco or Los Angeles?
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
G-d knows what you might have there in your record and you, of course. We do not. Hence, you should ask G-d this question or yourself, not us.
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