No, you don't need the 1095-C. If you did not have Mass Health, you need to answer NO to that question - otherwise, you will be prompted for a 1099-HC from MA.
1095-C and 1099-HC are not interchangeable. The first is for employer-based insurance and the 2nd is for Obamacare. Only Obamacare gets reported on your tax return.
When you did the federal return, did you answer NO to the 1095-A question? That is the Obamacare question. If you answered YES, go back and answer NO and delete the 1095-A and Form 8962. Instructions below. Go back through the MA return and answer NO to the Mass Health question. If you have employer based insurance, don't enter your 1095-C, keep it with your tax records.
How to delete forms in TurboTax Online
How to delete forms in TurboTax Desktop
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