Dragonborn has a few things to say about Morrowind's independence.
When speaking of (now defunct) House Hlaalu:
Dragonborn also notes that the Redoran are the rulers of Morrowind in the Empire's absence, even though the House Council remains.
The only reason I pull pack from saying that Morrowind is completely independent is because we were never given a formal secession notice like there were for Black Marsh, Elsweyr, and Alinor. Therefore I'd say the most conservative position you could take on this is by saying that Morrowind maintains a de facto independence from the Empire, if not a de jure independence. That means that while the Empire might still claim for itself the right to rule Morrowind, nobody in Morrowind acquiesces to this claim.
Of course, the same could be said for all the provinces, even the provinces (except Hammerfell, who didn't leave the Empire but was cast out) that formerly declared secession from the Empire. Even with a formal secession of a nation, that doesn't mean the Empire recognizes such a secession.