You generally pay tax to the state where you live and to the state(s) where you earned income.
In your case, you lived in Louisiana in the first half of the year, thus, generally, you would report dividends, interest, and gains earned while you lived in Louisiana (note: The interest and dividends were received from obligations of a state or political subdivision of a state other than Louisiana. Obligations of the State of Louisiana, its political subdivisions, or public corporations created by them and their constituted authorities are exempt from Louisiana taxes, so don't include these in your Louisiana income).
Thus, if the interest and dividends were reported only at the end of the year, you would prorate them for much time you lived in Louisiana (assuming they were taxable, as note above). You can prorate based on number of days (note this in your tax files, in case anyone ever asks).
If the capital gains were because of a specific sale (like a stock sale), then the gain belongs to the state where you were living at the time of the sale. Otherwise prorate the gains as above.
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