Yes. If you have an HSA-qualified high-deductible health plan (HDHP), you’re allowed to contribute tax-free money to a health savings account (HSA). In most cases, you cannot contribute to the HSA if you have other health coverage in addition to the HDHP. But the IRS allows people with HDHP coverage to contribute to an HSA even if they also have various types of supplemental coverage — including supplemental accident insurance.