Living outside the US, didn't earn any money in the US. Not sure what to give as my state of residence.

[TomK]

If you are the resident of a foreign country and have not lived or worked in one of the 50 states, then you do not file a state income tax return.

Using TurboTax, in the Personal Info section for your name, for the state of residence dropdown, scroll down to the bottom of the list and choose Foreign or US Possession.