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?
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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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I have never seen a problem arise from submitting a background check request nor an FBI check. As a matter of precaution, as a reason for the request, I write "for my own review."Ask a similar question