The general rule is (and it applies, in your case): your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state. You will have to file a non resident OH state return and pay OH tax on the income earned there.. You will also file a MO full year resident return and calculate tax on ALL your income. MO will give you a credit, or partial credit, for the tax you pay OH. So, there will be little or no double taxation, but you have the cost and hassle of filing two state returns. Do the nonresident state return first. Doing the returns in the correct sequence insures that your MO return will include the credit for the tax you pay to OH.
Be advised that Ohio does a convoluted tax calculation for non-residents/part year residents. It calculates tax on total income, then it calculates a non resident/part year resident credit, which it subtracts from the tax it calculated on the total income. The credit is calculated as your non-Ohio income divided by Total adjusted Income multiplied by the total tax. TurboTax (TT) does this by allocating your income as either Ohio or non-Ohio. TT will ask you, item by item, in the state section, how much of your other income is Ohio or non-Ohio income.
