You did not state if you were renting the TN house. Let's go with worse case scenario. CA has the right to tax residents of the state on any income they receive from any source. Let's say you're renting the TN house and you show a profit. You would report that on your Schedule E on the Federal return. TN has no state tax, so there's that. The income from your Form 1040 would flow to your CA return and you would pay CA state tax on it.
Rental properties tend to show a "paper loss" each year due to depreciation. Chances are, you won't show a profit.