If you are a MA resident for all of 2019 you will file a MA resident return (Form 1), even though your new address is in RI. For 2020, you will still pay MA tax on income you earn inside of MA. You are also liable for RI tax on the same income; however, Rhode Island does give you a credit for the tax you pay to Massachusetts on the income you earn in MA. What I have typically seen is that the credit covers the RI tax liability because I believe MA has a higher tax rate than RI. But you may want to check on that. If RI tax rate is a bit higher than MA then you would want some RI tax withheld also (if the company can do so) to make sure that you don't have a shortfall at the end of 2020.
But for 2019, no real consequence. You will file for MA only as a resident.
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