Yes, in order to file compliant tax returns in Michigan and Massachusetts that's exactly what you will have to do.
As @JohnB5677 said. to do it in TurboTax, you will need to use the Desktop version of TurboTax that will allow you to create and efile your Federal Married Filing Joint return and your Michigan Married Filing Joint return.
You can then prepare a Massachusetts return Married Filing Separate and claim a credit for Taxes Paid to Another State on Schedule OJC on your income that was taxed on the Michigan return to avoid being double taxed on income.
TurboTax will only allow you to efile one of the state returns, so you will need to mail in the Massachusetts return with a copy of the Federal return and a copy of the Michigan return to show the income taxed by Michigan.
