If I filed a NY State return in 2015 and didn't live in NY State in 2016, do I have to file a return for 2016?

If you didn't live in AND have any income from NY state in 2016, then no.

Income includes any taxable income, like wages, unemployment, or pensions.

Here are the NY state instructions to determine if you need to file if you have any income from NY state.

https://www.tax.ny.gov/