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!
