State tax filing

Yes.  You will complete your federal return first, then TurboTax will allow you to complete both states.  When you are in the 'Personal Info' screen be sure to select the second state that you will need.  Be sure to enter the income and withholding appropriately in your W-2 screens.  See the image below.

You can begin either state first since you are a part year resident in both states.  Double check your income to be sure you have the correct state wages and taxes, etc.