Write off? You write off EXPENSES, not INCOME. I believe what you are asking is whether you can deduct the operating costs of the property from the income. As long as the expenses are legitimately related to the property you can. Also, you would have to rent to your relative at fair market value (or close enough to it that it wasn't questioned). You can't throw your brother in there for $500/month when the market rent is $2000/month (and make up the difference elsewhere...) and deduct the manufactured loss.
Note: I am not giving legal, accounting or tax advice of any kind. I am merely stating an opinion based on the fact pattern described. Please consult with your accountant or tax specialist for specific, accurate information.