Yes, you should file a resident tax return for Pennsylvania (PA), and a non-resident tax return for both New Jersey (NJ), and Maryland (MD).
"Pennsylvania residents are subject to Pennsylvania personal income tax on all Pennsylvania taxable income classes, both Pennsylvania and non-Pennsylvania source income, though they may qualify for a resident credit for tax paid to other states on income earned outside of Pennsylvania."
Commonwealth of Pennsylvania website: Personal Income Tax Guide - Brief Overview and Filing R...
First, first make sure you've filled out the About me or Personal Info section correctly.
- Go to the Personal profile screen, scroll down to Other State Income, and select Edit.
- On the Did you make money in any other states? question, answer Yes and make sure your nonresident state(s) are selected from the drop-down.
- Select Continue to return to the Personal profile screen.
To ensure accurate calculations, always complete the nonresident return first if filing in multiple states because your resident state might give you a credit for any taxes paid in that situation.
For more information, please see TurboTax FAQ: How do I file nonresident state return?
You can leave your employer withholding just as they are if you want, it is perfectly fine.
However, you may also consider If you live in a reciprocal state, submitting an exemption form to your employer so you don't have to file a nonresident return next year. PA, NJ & MD do, have reciprocal tax agreements.
A state reciprocal agreement between two states 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 more information, please see TurboTax FAQ: What is a state reciprocal agreement?
For more information, please see TurboTax FAQ: Which states have reciprocal agreements?
Form MW507 - Employee’s Maryland Withholding Exemption
Form NJ-165 - Employee’s Certificate of Nonresidence In New Jersey
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