I would think any state/local withholding should show up on your W-2. if not there's no way to claim it. An employer is not required to do this
If an employee resides in one city and works in another, they may be required to pay local taxes for both cities. Courtesy withholding is an optional benefit where employers collect local income tax for employees who live in another city. Through courtesy withholding, employees don’t need to pay local taxes separately, as the employer deducts these amounts and pays them on the employee’s behalf.
If the employee lives in a different state, the employer can also do courtesy withholding for state income taxes.
check with your employer for what there policies and procedures are.
