"Was [name] covered by a High Deductible Health Plan (HDHP) in [the previous tax year]?"
The purpose for this obscure question about the previous tax year is to determine if you took advantage of the "last-month" rule in your HSA in that year. That is, if you had an HSA in the previous tax year and you used the full annual HSA contribution amount (instead of having it pro-rated by the number of months that you had the HDHP coverage), then you would be required to keep your HDHP coverage (your High Deductible Health Plan, which is required for an HSA) through the "testing period", in essence, through all of the current tax year.
If you did have HDHP coverage on December 1st of the previous tax year, then answer by whichever it was: Family or Self.
Note that some taxpayers are getting a "break in coverage" message. If you were in the HDHP coverage for all of the previous tax year or for all of the current tax year or for none of of the previous tax year, then you can safely answer "None" to avoid this message, because the last-month rule doesn't apply to you anyway.
[Edited 3/11/2020 4:27 pm CDT - made year neutral]
