The IRS only wants the Federal return and does not want a copy of the state return. But some state tax agencies also want a copy of the Federal return (or certain forms and schedules from the Federal return) to be enclosed along with the state return to verify the figures you used on the state return.
As @Mike9241 referred to, the Filing Instructions that print out with your returns should tell you what to send. There may be a page of Federal Filing Instructions and a page of State Filing Instructions.
The Filing Instructions should also have the mailing addresses to use.
But why are you filing paper returns by mail? If you are due a refund, manual processing could delay it for months.
Why are you not efiling? If you're having a problem efiling, we may be able to help you efile.
You only mail federal to the IRS. California sometimes wants a copy of federal behind the CA 540 return so if it prints out 2 copies of federal 1040, one goes with state. And it should say on the Turbo Tax cover sheet.