Which method is more acceptable or more common for a person who is a part-year resident in two states and has income fully withheld in one state for the entire year?

When you are a part-year resident of two states, you allocate your income to the state that you were a resident of when you received the income. TurboTax will guide you through allocating your income when you move from one state to another during the year. When you are preparing your part-year resident tax returns, you will allocate your income to the state that you were a resident of when you received it. 

If you've already entered your personal information, review your entries to help ensure that TurboTax will help you create the correct part-year tax returns. 

1. Open TurboTax and select My Info
2. A Personal profile summary screen will pop up
3. Select Revisit by your address
4. Scroll through the screens to help ensure that you have the correct answers for your state of residence and choose that you live in another state. A new section will appear asking for your previous state of residence. Select the other state that you live in.
5. Scroll down to Other State Income and select Edit
6. Check your answer for Did you make money in any other states? Answer the questions and select Continue.

After you complete your federal tax return and you move to the State Taxes sections, both of your part-year state returns will be listed.  Prepare the state that you moved from first, then the state that you live in.

Please visit this TurboTax Help articles How do I file a part-year state return? and How do I allocate (split) income for a part-year state return? for further explanation.

 I want to confirm that sourcing the income between the two states is the correct method and that the credit option should not be used in the described situation.

If living as a part-year resident in two states and being fully witholded only in one state (as the address was not changed on the tax withholding), is it correct that the state income tax report should be based on actual dates of residency in each state?

In other words, should the amount withheld to the previous state after moving to a new state be refunded? (and should not be used as a credit to a new state)?