You will be doing a part-year resident return for each of the two states this year.
This FAQ explains how to file part-year resident state returns in TurboTax: https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return
Also, you may be able to deduct some moving expenses. This IRS reference explains the rules for that: https://www.irs.gov/taxtopics/tc455.html
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
