Since you work in Kansas City, MO, you have to pay this tax. The Kansas City Earnings Tax is for anyone who either works or lives in Kansas City, MO.
Please see the tax's description at the KCMO website.
However, note the following at a KCMO FAQ (look under Individuals:(
"Your employer should withhold the earnings tax if you work in Kansas City, Missouri. Your W-2 (or your paystubs) will reflect tax paid through payroll deductions. You do not need to file a return if the amount in Box 19 of your W-2 equals 1% of Box 1.
Your employer may be willing to withhold the tax if you are a resident but do not work at a location, or perform services, in Kansas City, Missouri. Please check with your employer for more information."
If your employer withheld the tax (the 1%) then you are done; if not, if you answered the questions in the Missouri interview about this city tax, then look in your Missouri output for the form, print it and mail it with you payment (or look online for online payment options).
I lived in KCMO for 5 years and used Turbotax every year and it never once told me I need to pay this tax (employer was not in KC so didn't withhold). After moving I just received a collection notice saying I owe back taxes plus interest plus late fee. I have friends who use TaxAct and were informed of the tax. I feel this is an error on TurboTax's part: what will TurboTax do to remedy this issue so I don't have to pay the extra fees?
If you lived in KS city, you should have paid tax. See How to submit documentation for accuracy guarantee claims.