If don''t own my home and I am still paying mortgage on the house in the State of California, do I need a living trust or will for my home investment?

I assume you are now renting out the home you previously occupied in California and you are still paying the loan which is secured by the house.  If you have equity in the house, and you don't want your heirs to face probate administration, you should consider a revocable trust, yes.