To conduct an HSA rollover, contact your current HSA provider, such as a bank or mutual fund company, for the rollover. Health Saving Account custodians will send your funds via a check or to your personal bank account. The important thing to take care of is that you have 60 days to deposit your funds in the new Health Saving Account. After 60 days, it will be considered a taxable distribution, and the IRS will subject you to income taxes and a 20% penalty.