Your Federal tax situation will not change, but your state tax situation could.
Depending on the states involved, you may have to file more than one state tax return during the year that you move or even later years if you live in one state while working in another one. If and when you move, just be sure to keep good records of the dates involved and where you were living and working. Also, be sure that your job is withholding state taxes for the correct state.
TurboTax will help you work through the state situation by asking questions about your state of residence and where you earned income.
Here are some TurboTax articles that may be helpful to read:
How do I file if I moved to a different state last year?
How do I file a part-year state return?