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Because your tax home is CT you will file as a CT resident and MS non-resident. You will receive credit for the taxes you paid in MS on your CT return.
Here is a link to MS Tax Commission where you can get forms and instructions for completing you MS tax return.
Nevada has no state income tax.
You will qualify, it appears based upon your question, for the foreign income tax credit for the next 3 or so years. I am attaching a link that you might find helpful in that area:
If you have further questions on this topic, be sure and get back to me.