Did you go to CA and do the work there?

or is the company that paid you for work that you did for them in NC just located in CA?

Here are more details:

For the first couple of months of 2017 I worked as an independent contractor for Cisco Systems, but technically I worked through a third party contracting firm. I worked as a 1099 independent contractor, but this other firm is who paid me and that firm is also based in California, same as Cisco.

However, I did NOT work in California. I did all my work remotely from NC. 

The notice I got says the California Franchise Tax Board thinks I should have filed a CA tax return and if I do not respond they'll send me a bill. I filled out their questionnaire and responded but even by their own "rules" I don't think I made enough gross money (I made $25,600.00 as a contractor that year) to meet their threshold. 

Frankly I never knew of any situation where I'd be responsible for another state return if I never actually worked in that state. I was only paid FROM that state.

Somehow the CA FTB knows of your income (most likely CA appeared in boxes 16-18 of your 1099-Misc).

Returning the questionnaire should take care of the problem.  

The CA filing requirement goes by your total income, not just your CA source income. Ref: https://www.ftb.ca.gov/file/personal/residency-status/part-year-and-nonresident.html