Enter the information as if you received a single W-2, but enter each state's Box 15-20 information on a separate line.
You'll be preparing a part-year resident tax return in each of the two states. TurboTax will allot your state withholdings accordingly.
This TurboTax FAQ explains how to file part-year returns: https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return
**Answers are correct to the best of my ability but do not constitute tax or legal advice.