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Claiming income/deductions on an illegal apartment
A basement unit would typically rent for less than similar space on a higher floor.  Taxwise, you should be claiming the income, and expenses via schedule E, as if it were legal. Keep in mind, Al Capone was convicted on tax evasion  not his other illegal activities. As long as you treat it as a legitimate business, a rental unit, you will be good with the IRS. The local building department will fine you if they find out.