Suppose you have a banking account opened in state X and you live in state Y. If you earn interests with the account opened in state X, can that be considered income from state X, or should it be considered as income from state Y?
Most (if not all states) in the US are only interested in source income. If you worked in that state they want to tax it. Many states have reciprocity agreements with neighboring states to exempt income earned when a person works in lets say Virginia, but lives in a state that touches Virginia.
Most states don't consider interest and dividends for individuals as source income. They don't care where the bank or mutual fund branch is located, or headquartered.If it is interest from a business they will allocate it to the state where the business is located.
If you may ask you to allocate the funds between two states if you move during the year, but most people will just divide the interest and dividends based on the number of days in each state unless there is a way to directly allocate the funds to a particular state.
Consider this: Where is the money when it is in a bank with multiple branches? The money is only electronic, and your actual "$'s" may be in a federal reserve branch. Pension funds are invested in projects all over the US.