Actually, some states allow filing before you get the ITIN. You could file your return now writing "applied for ITIN" in the field and then send the ITIN to the state as soon as you get it.
MA is one of those states for example.
However, it would probably be less of a hassle to wait for the ITIN and then file. Just be sure you pay any taxes you might owe the state as soon as possible (if you haven't done it already) to avoid penalties/interest.