No, you should not have to file a state tax return if you did not live or earn wages in that state during  2018.

The most common use of Form 1099-G is to report unemployment compensation or any state or local income tax refunds you received. 

If you received a Form 1099-G for unemployment compensation you will report this on your 2018 tax return.

If you received a Form 1099-G for state or local income tax refunds yo will have to report this on your tax return for 2018 only if you itemized your deductions for 2017.