No, you will not need to attach your California state return to your New York state return. Your mailing instructions will explain what to mail.
If you are using TurboTax CD/Download software, the first page in your printout package will be the File by Mail Instructions, which will provide the mailing address and what form, if any, you need to include.
If you are using TurboTax Online, there should be a filing instructions document that prints out with the paper copy you'll file. However, you will need to pay before you will be able to print and see your filing instructions page.
