Applying for ITIN number

Hello. Since I am applying for an ITIN for my wife, I understand that I would need to attach form W-7 along with other documents to my federal tax return. However, I want to ask if I would need to attach the same things to my state tax return since they are mailed to 2 different places and I'm afraid the tax center in California would not accept my return if the SSN box is left unfilled.