You do not need to file a New Mexico state tax return for the 1099 G.
The 1099 G was issued by New Mexico for the refund of state taxes you received in 2015. The only place it is considered as income is on your Federal Tax return and it is only considered income on your Federal Tax return if you itemized deductions in 2015 and included the state taxes paid to New Mexico in your itemized deductions.
