State tax filing

It depends.  If this house was your main home for 2 out of the last 5 years, you could potentially exclude the gain up to $500,000 if you are married filing joint, or $250,000 if you are any other filing status.  If you did not reside in the home during this period and it was held for investment purposes, you may need to pay taxes to California as these exclusion amounts would not apply to you. 

California taxes at ordinary tax rates and does not have any capital gains tax rates.  You would need to file Form 540NR.  The Franchise Tax Board is currently updating it's tax rates schedule  (California Tax Rates) but I have attached a link to the tax rates for 2018 to help you estimate your tax based upon your specific situation and gain from the sale of the property. 2018 California Tax Rates.

As for New York, you will be taxed on the gain on the sale of property if there is any, but New York allows you to claim a credit against your New York tax for any taxes you pay to the other state on the same income.  In order to do this, you should prepare the nonresident California return first in the TurboTax program.  Once you have determined the amount of tax due to California, you will enter this amount into your New York return on Form IT-112-R, New York State Resident Credit.  In order to enter this information in TurboTax, when you are preparing your New York return, you will go to "Taxes Paid to Another State" under the New York credit and taxes section.  When you reach the "Other State" page, you can enter CA, continue to the next page, and then enter the tax paid to California.  This will ensure you receive the credit in New York for the taxes paid in California.