You need to file part-year resident forms in both states. You enter the full amount of the 1099 form income in the federal return. When you do the state returns you will be asked to allocate that income to each state based on where you earned it and more importantly how long you lived in the state.

As a practical matter, you can allocate the income based on how long you lived in each state if it was somewhat evenly distributed during the year.

Thank you for the information - it makes sense to allocate based on time spent in each state. As a follow-up question- my 1099-DIV and 1099-B have dates associates with each dividend / sale of assets listed on the form. In that case, should I go by the date and which state I was in at the time, or would it be best to still allocate equally?

Yes, you should go by the dates that you have on the 1099-DIV and 1099-B to accurately allocate the income to each location. That would be the most accurate.