Do I need to include my spouse's income in total household resources if we only lived together part of the year?

Yes. You can use Form 2105, Michigan Homestead Property Tax Credits for Separated or Divorced Taxpayers, to help you prorate the share of taxes or rent used to complete the homestead property tax credit.  You should also submit a completed Form 5049, Worksheet for Married, Filing Separately and Divorced or Separated Claimants.