You would generally only take a credit for taxes paid to another state on a Part Year or Nonresident return if the amount of income that is being reported as taxable to the state includes wages that were actually taxed by another state.
Example: John's W-2 shows total wages of $30,000. That is all the money he made for the year. In the state section of his W-2, it lists $30,000 as being taxed by GA and $5,000 as being taxed by AL. In this case, his GA wages ($30,000) include income ($5,000) that was actually earned in and taxed by AL. On his GA return, therefore, the income that is reported as GA source income, and that is used to figure the appropriate percentage for his GA tax liability, actually includes income that is taxable to and taxed by another state. Because this amount (the amount used to figure his GA percentage) includes income taxed by another state, he would be able to take the credit for taxes paid to AL on his GA return.
The only reason that he can take this credit is because GA actually taxed all $30,000 of his income during the year and he is reporting all $30,000 as taxable on his GA return. Some states (such as New York) require employers to list all of your income on your W-2. However, the state doesn't actually tax all of the income. It is just listed on the Form W-2. You can only take this credit if the amount listed is actually taxed by the other state.