A reciprocal agreement, also called reciprocity, is an agreement between two states that allows residents of one state to request exemption from tax withholding in the other (reciprocal) state. This can save you the trouble of having to file multiple state returns.
For example, let's say you live in New Jersey and work in Pennsylvania–two states with a reciprocal agreement. You can ask your employer to stop withholding Pennsylvania taxes. If your employer stops withholding Pennsylvania taxes, you would only have to file a New Jersey return.
The reverse would also be true. If you lived in Pennsylvania and worked in New Jersey, you can ask your employer to stop withholding New Jersey taxes. In this scenario, you would only have to file a Pennsylvania return due to the reciprocal agreement.
If your employer has withheld taxes for the work state instead of the resident state, you'll have to file for a refund from your work state. You'll still file your resident return that also includes that income and pay tax on it.
TurboTax handles reciprocal states and will generate the correct state(s) based on your personal information and your W-2.
You can see which states have reciprocal agreements and, if you live in one of those states, the exemption form you can file. If you file an exemption form to not have withholding form that state, be sure to ask your employer to withhold taxes from your resident state.