Usually no, unless they are gang related and there is an investigation, but this is highly unlikely.
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In general, there are no tattoo laws, however, certain tattoos could raise the presumption of affiliation with certain gangs, which if proved, could affect the application.
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The man you refer to probably had affiliations with known gangs, and the tattoos were what tipped off CIS. Otherwise, tattoos are NOT a grounds for denying immigration relief.
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