Michigan Statute 206.110(2)(a) defines Michigan-sourced income (of a non-resident) as:
(2) For a nonresident individual, estate, or trust, all taxable income is allocated to this state to the extent it
is earned, received, or acquired in 1 or more of the following ways:
(a) For the rendition of personal services performed in this state.
http://www.legislature.mi.gov/documents/mcl/pdf/mcl-act-281-of-1967.pdf
Therefore the remote work you performed in Michigan is Michigan-sourced, even though performed for an out-of-state employer.
Therefore your remote earnings are taxable both by MI - because it is sourced there - and by NY - because NY is your domiciliary state and thus able to tax all your income, regardless of source. And you are eligible to claim the other state credit on your NY return.
In TT, be sure to complete the non-resident state return first, before the home state return, so that the program can calculate and apply the credit correctly.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
