In the Federal section you do not enter the state in the dividend area.
Then if you lived in two different states during the year, you will either look at when the dividends were actually paid or pro-rate it based on days lived in each State.
So for example say you had $1,000 of dividend income (paid throughout the year) and State A you lived in 3 months or 255 of the time, and state B 75% of the time.
Report 25% of dividends to State A --$250
Report 75% to State B --$750 in my example.
