I got a new job and was able to put my wife on my non HDHP insurance starting in April. I also had a non HDHP at my old job for the first 3 months of the year, but my wife was not on it. I am filling out the 8889-S for my wife's portion of our taxes and it is asking for a month-by-month coverage status. Should I select "self only" for the first three months and then "none" for the remainder of the year since she was not covered by an HDHP from April through December? If I select "Family" it increases our refund, but I don't think that's accurate.
Go back to the Step-by-step interview.
When answering the questions on your wife's HSA (Federal->Deductions & Credits->Medical->HSA MSA Contributions), on the screen "Was [wife's name] covered by a High Deductible Health Plan (HDHP) in 2017?", answer "yes". Then on the three new lines that appear below, answer "I had different plan types at different times of the year."
See screenshot below.
This will cause the next screen to ask you for a month-by-month report of her HDHP coverage.
Your wife's coverage for the first three months (but see note below) is whatever type of HDHP policy that she had: Family or Self. She probably had Self, but if she had any dependents on her policy, then she would have had Family.
You are correct that once she passed on to your non-HDHP coverage, she should enter "none" for each month.
NOTE: your type of coverage is determined by the coverage on the first day of the month. Thus, if your wife went on your policy on April 15th, she would have had four months under the HDHP (Jan - Apr).
NOTENOTE: please note that the HSA belongs to your wife, not her employer. She does NOT have to close the HSA just because she changed insurance coverage. It's true that so long as she is under non-HDHP coverage, she can't contribute to her HSA, but she can continue to spend from it on qualified medical expenses with no penalty until the money is exhausted.