No, although your payroll deductions will automatically stop when you reach the maximum allowed for your circumstances. Otherwise, you alone are responsible for monitoring your eligibility for the HSA, the maximum amount of contributions that you can contribute and whether the expenses that you submit are eligible for reimbursement. Neither the company nor the HSA administrator makes these decisions. If your federal income tax return is audited by the IRS, you may be required to prove your eligibility for the HSA, as well as the level of contributions made and distributions received. Therefore, it is very important that you educate yourself on these issues and retain appropriate documentation.
Helpful information is available on the IRS website (irs.gov), including Publication 969, which covers HSAs. You also may want to consult with a tax professional.