No, you only need to mail your federal items to the IRS - you do not need to include anything related to your state.
If you e-filed your return, then all you would need to mail to the IRS is the payment voucher (Form 1040V) and your check. You do not also need to mail your entire tax return.
If you are filing by mail, then you would need to mail your signed tax return along with a filing copy of any W2s or 1099s attached to your return. You would also need to include the payment voucher and check.