It depends.  Most states, when determining your tax as either a part-year resident or a nonresident, first determine how much tax you pay on all of your income, and then prorate the amount of tax on the percentage of income earned in that state.  With a source of income such as dividends, it is possible that a manual entry is required in the PA return, but the same percentage can be used to determine the amount of dividends that are taxable in PA.

Of course, Texas has no state income tax, so there is no filing requirement in Texas.