That message is telling you that the return you did in TurboTax was e-filed and that it went through, so now the State of Michigan has your return.
No, you do not need to sign or send in the return, it has been e-filed, so it's done.
Yes, the Michigan Home Heating Credit was attached to your Michigan State tax return, so that was sent in as well. No, you do not need to mail anything in.
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