Did you place your hand on a bible and swear?
If not, then as far as I know you have as much legal obligation to tell them the truth as a cop does when he's talking to the citizenry.
If it's none of their business, give whatever answer you think is appropriate.
*Let me hasten to add that I have no idea if a rental agreement is any sort of legal document in your state in regards to the truthfulness of any statement.*