Yes. If you have a health savings account (HSA), your contribution to a self-only plan is permissible up to set annual limits (in 2019 it’s $3,500, plus $1,000 if you’re age 55 or older by year end). Alternatively, if you have a dependent under the HDHP, you can contribute to an HSA up to the limit for family coverage.
Return filed by a married person who does not file a joint return. Filing separately may save taxes where each spouse has separate deductions, but certain tax benefits require a joint return.