What's important is when you receive the income, not where the income is from. The new state cannot tax income that you received before you lived there. The new state can tax any income that you receive while you are living in the new state, no matter where the income is from. For example, if you work in the old state after you have moved, the new state can tax the income that you earn for working in the old state while you are living in the new state. If you sell a home that you own in the old state, and the sale closes after you have moved to the new state, you would have to pay tax to the new state on your gain from the sale, even though the sale took place in your old state.
