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You do need to file a CT extension separately.
I am researching OK.
Oklahoma "honors" the federal extension which means you can just enclose a copy of the federal extension when you send in the late return. Not sure how you do that when you efile, in theory you check a box and say "I have an IRS extension". If I were in your shoes, I would send in OK FOrm 504-I postmarked tomorrow and CT form 1040-EXT postmarked tomorrow. Neither of these states are "automatic extension" states.
it can't hurt.