Yes. You can file a NJ-1040NR income tax form to back any excess "exit tax". TurboTax will create a NJ-1040NR if you tell TurboTax you are a nonresident with income from NJ.
In TurboTax online:
- Click on My Info in the left column
- Scroll down to Other State Income
- Say YES to Did you make money in any other states?
- Select New Jersey in the dropdown menu
New Jersey follows federal law in that you may be entitled to a home sale exemption if you owned and occupied a home for two years in a five year period.
See: Topic No. 701 Sale of Your Home