Yes, you will need to file a Part-Year Resident return to both Pennsylvania and New Jersey. In the Personal Info section, indicate that you lived in both states during 2024.
Although you have no earned income, you will allocate your pensions, Social Security, and any other income you have between the two states, based on the time lived there. You can divide the yearly total by 12, then multiply by number of months lived in each state.
In your state interviews, you will need to manually adjust the Federal amount that applies to that state.
Here's more info on How to File a Part-Year Resident Return and Allocating Income for a Part-Year Resident.
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