Can you still get a federal tax refund if you didn't pay state tax the year prior?

You can file a federal tax return and get a refund regardless of the status of your state taxes. If you owe overdue taxes to the state and they have gotten around to it, the state can intercept your federal refund. So, your refund might go to paying your overdue state taxes instead of being sent to you. But unless you file a federal tax return, no refund will be generated and your state taxes will not be paid.