The company I work for is located in Detroit, but I primarily work from home (outside Detroit). How do I file my City/State income tax to exclude the days I work from hom

You have to file a nonresident return for Detroit and indicate the amount of wages you earned wages inside of the city. You can divide your total wages by your total number of workdays and multiply your daily rate by the number of times you worked in Detriot. 

Wages earned as a non-resident while working from a location outside the City of Detroit are not taxable to Detroit. If Detroit taxes were taken out of your paycheck the entire year, you will get a refund of the local tax paid while you were not working in Detroit.

Please follow the steps below to file a part-year Detroit return:

1. Click on State.
2. Click Continue next to Michigan.
3. On the screen Which Cities Did you Live or Work In? Click Detroit.
4. Click that you need a Detroit non-resident return. 
5. Continue through your return.
6. On the page, A few things before we wrap up your state taxes, click Start next to Michigan City Tax Returns.
7. On the page, Income Apportionment, enter the amount of wages you earned while in Detroit location. 
8. Follow the on-screen instructions.