State tax filing

Unfortunately, you are subject to taxation in both states

While Pennsylvania does have tax reciprocity agreements with several states, Delaware does not participate in any of these agreements. Delaware taxes residents on the income they earn in Pennsylvania. Pennsylvania taxes non-residents on the income they earn in the state.

So you are not taxed twice, you are allowed a credit for the taxes paid to Pennsylvania. The net effect is that your overall state tax rate will be at the higher rate between the two states. 

When you prepare your tax returns, you will need to prepare your PA return before you prepare your DE return

For more information, follow these links:

Delaware on Out of State Income

PA Who Must File 

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