Employers typically are required to withhold tax in the city where there are situated. Your Ohio locality where you live should recognize the tax that was already paid.
All residents of a city with an income tax must file a city return and usually pay that city some tax, even if their work city withheld tax. You normally only have to file a return in the city you live in. It is not necessary to file one in the city you work in, if different.
Oakwood City gives you credit for city tax withheld and paid to other cities as long as you provide the W2 as proof.
