Your state of domicile is the place of your permanent residence on December 31. In your case, it's probably your home country. Students are considered "temporarily absent" from their permanent home.
TurboTax allows you to choose "Foreign or U.S. Possession" as the state of residence. It's the last choice in the dropdown.
Some states consider you to be a resident if you spend a certain amount of days in the state, generally around half the year. If you worked and had state tax withheld, you should choose the state you lived in on December 31 as your domicile state so TurboTax can prepare an accurate state tax return (if needed).