Yes, any payments derived from oil and gas production located in New Mexico to a non-resident of New Mexico must withhold tax from those payments, and file form RDP-41374. Or "any other income and withholding information return that includes New Mexico income tax withheld must be sent.”
Yes, New Mexico does. Learn more about combined state and federal filing. In most cases, if you participated in combined filing for your 1099s, then you do not need to send 1099s to the state’s Taxation and Revenue Department, they should already have a copy.
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