Which state do I get my business license in?

Really confused on licensing requirements for my business.

I reside in CA, and I work out of my home, managing my business and
keeping its books.  I invest in property in New Mexico and rent it
out.  The property is profesionally managed.  My income is from the
rentals I have in New Mexico.

Technically, if I want to play things by the book, do I need a
business license in CA or New Mexico or both?  What is the locality of
my business?  I really don't have an office in New Mexico; just a
private residence for a renter.  I'm "doing business" in my home in
CA, but I'm also doing "business transactions" in New Mexico, so
what's required here.  What about a fictitious business name
statement?