It depends on whether your home office expenses are from being self-employed or from being an employee. When you prepare part-year state returns, you have to allocate the income and expenses between the two states.
If you had $200 of expense for the year and lived in each state for 6 months, you could allocate $100 to each state return. Each return will show the full amount on your federal return and you enter in the amount you allocate to each state which total to the full deduction. If none of the expense belongs to that state, enter 0 and then enter 100% of the expense on the other state return.
If you are self-employed, home office expenses go on Schedule C. Here is how to enter multiple home offices if you are self-employed.
Employees working at home for an employer cannot deduct these expenses on the federal return. DE doesn't allow the deduction on the state return but PA does. So, if you are claiming office expenses as an employee (not self-employed), only the expenses in PA can give you a tax deduction.
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