Some states may allow people to file state returns without ITINs for the moment. I lived in North Dakota and I called the state tax office beforehand to ask about what to do given my pending ITIN application and the forthcoming deadline for state tax filing. They told me to file the state return without the ITIN and attach a copy of my ITIN application. Once my ITIN is approved, I would just need to contact the state tax office again to add the ITIIN. So I filed my state return and received the refund in early July, although I am now still waiting to hear back from my ITIN application and federal tax return 6 months after I submitted them through a field IRS office.
