Generally, the IRS doesn't care so long as all income/expenses are reported and all taxes are paid. However, it depends on the laws of the state you are in, and they can differ quite significantly from state to state. You should seek legal advise from a licensed professional in your state.
Note that if only one of you is reporting rental income/expenses, this will create reporting issues when you go to sell the property, since only one of you will have taken depreciation on the property. That's one of many reasons why professional help is highly recommended.
