State tax filing

So does this mean I should pay the Ohio tax even though I was living in Michigan at the time I did the work in Ohio, then take a credit for the amount paid to Ohio on the Michigan state form?

 

And when it asks for the amount that is being taxed by the other state, do I put in the full W2 amount since NY and Ohio both calculate taxes on the full wage earnings?  Or do I put the amount that represents the percentage of time I spent in that state?