NM is messed up on their "Resident " vs Nonresident definitions..and at partially at odds with most or all other states in the entire country. (yeah...opinion)
See comments that follow below:
Yo! They should NOT be filing NM as partial year residents in 2019. NM says if you were PHYSICALLY PRESENT IN THE STATE for more than half the year, you are considered a resident.
Since the OP moved out in August, they are definitely full-year residents for 2019 NM tax purposes. They can use the allocation form only if they earned any income (including a pension) in SD after they moved.
When we retired and moved out of NM, we were just on the cusp of this half year. Turned out that I could file as a partial year resident, but my husband had to file as a full-year resident because he went back to the state a couple weeks for business consulting, just enough to put him over the physically-present limit. So I had to calculate how much of our jointly-earned interest and dividends was attributable to both of us for part of the year in NM, to me (in TN), and to him (remainder of the FULL year in NM). Nightmare!
I agree, the NM instructions are fairly two-faced about that...and confusing.
Person(s) first moving "into" NM are considered Part-Year, even if in-state more than 185 days as a "First-Year resident" .
Yet those moving out are full year if they were in-state more than 185 days.
You are a New Mexico part-year resident if you meet all of these conditions:
• You were a New Mexico resident for part of the year.
• You were not physically present in New Mexico for 185 days or more.
• On December 31, you were no longer domiciled in New Mexico and you had moved to another state,
intending to maintain domicile status in that other state.
For purposes of the Income Tax Act, you are a New Mexico resident if either of the following are true:
• Your domicile was in New Mexico for the entire year or;
• You were physically present in New Mexico for a total of 185 days or more during the tax year, regardless of your domicile.
Pages 3&4 of the PIT-1 instructions for 2019: