The 1099-G from California was from a refund of state taxes you received from California in 2016 for tax year 2015 and not income attributable to California.
As long as you enter the 1099-G into TurboTax for 2016 and answer all questions, TurboTax will determine whether or not the state tax refund is taxable on your federal return.
If you have no other California income and did not reside in California for all of 2016, then you are not required to file a California State return.
