So I worked for the same company in two different states. Given that I was a part time resident, would I need to figure what my pay was for both states?

Yes.  You can use your pay check stubs to determine how much was earned in each state during each residency period, if your employer didn't split it out for you on your W2.  Complete your W2 by adding an additional line for a second state to enter both the correct wages and the correct withholding for each state.

When you begin your state returns be sure to select part-year residency.  TurboTax will then ask the dates and allow you to put the income earned in each particular state or carry it from your W2 entry.

Sometimes an employer will issue two W2s, one for each resident period, but usually it's all on one W2 with all information on one or extra copies for state separated information.