Yes. You will file a TN non-resident return. More than likely "on paper" the rental will show a loss. Therefore no tax due. However, you still need to file a TN return to show that, since you have an income producing activity in TN.
Make sure you file your resident state return LAST. Otherwise, the program will not properly account for any tax agreement between the two states so you're not double-taxed. Remember, you still have to report the rental on your CA tax return to, since CA is your resident state.
