Can I file state tax form without ITIN? My wife is on H4. I am going to apply ITIN for her.

I don't think, I will get iTIN before April 15. My CPA is saying, you can put Applied Form on states form (CT and NJ) and file without waiting for ITIN?

Is this correct? If not, what I need to do? State Extension?

Most states no longer require any extension and, if you have refunds due from both, they are superfluous, because late penalties and interest will be due ONLY IF you owe taxes.

If you have refunds due from CT and NJ, just wait for your wife's ITIN, insert when you get it, then file late.