I lived in Brooklyn, NY from January - May of 2008. I was out of the country from May - December making no income. Do I file my NY State tax return as a full-time resident? Or do I fill out a part-time resident form? Thanks for your help!

You can be out of the state or country and still New York can be your "domicile" (where you plan to return, where you have a place of residence, where you are registered to vote, etc.). In that case, you would file as a full-time resident.

Unless you can somehow claim another "domicile", your residence is in New York.

If you are resident of NY or your stay away from NY was temporary or transitory, then you will report your worldwide income.