I live in RI but work in CT...I learned that I need to file a RI 1040MU....but don't know how to do that on turbotax

This RI 1040MU (related to claiming a state tax credit for states paid to another state) will generate automatically when you enter your out-of-state taxes (paid to CT) while entering your RI state tax information.

This amount will be transferred from your CT nonresident state income tax return (as long as you prepare your CT nonresident state income tax first). If this tax credit does not transfer automatically, you can enter it manually by selecting "Taxes paid to other states" during the RI state tax interview process (see screenshot).

You will want to work on your nonresident CT state income tax return first. You will then take a tax credit from your nonresident CT state income taxes on your resident RI state income tax return. (Please note that you will only get a tax credit for your CT state income taxes up to the amount of RI state income taxes that would have been paid if the income was earned in RI).  The credit for taxes paid to another state section will be at the end of your residence state's interview process.

Just follow the TurboTax guide when working on your states (remembering to do your nonresident state return first) and TurboTax will do all the calculations and credits to your resident states return

Here is additional information about filing in multiple states (select "see more answer" to view the entire attachment)

https://ttlc.intuit.com/replies/3300797