Check "Family". The following is a paraphrase of an answer by SuperUser Opus 17 if you want an explanation. Please feel free to post any additional details or questions in the comment section.
To be eligible to contribute to an HSA, a person must have
HSA-eligible insurance AND have no other medical insurance available to them
(except for certain narrow category of exceptions.) But an HSA, like an
IRA, is owned by one specific person. There is no such thing as a
"family" HSA, even though a person may have family insurance.
You are covered by a family HSA-eligible insurance policy, but your
spouse also has other medical insurance, so she is not eligible to make
contributions to an HSA owned by you. You are covered by HSA-eligible
insurance and has no other medical insurance, so you are eligible to make
contributions to an HSA. Because your policy is a family policy, you are
eligible to make up to $6750 in contributions for 2017.
The
fact that your spouse has secondary coverage means they can't contribute to an HSA, but
it doesn't affect your ability to contribute to an HSA you own as long as you
have no other secondary coverage.
ref:
https://ttlc.intuit.com/questions/4145011
