Are we required to notify our customers of an over contribution to a health savings account (HSA)? Are we required to distinguish between individual and family HSAs?

No, your bank is not required to notify HSA customers when they have exceeded their annual contribution limit.

Under the IRS requirements for HSA trustees, your bank generally should monitor contributions to HSAs and reject contributions that exceed a maximum amount, which is the sum of the maximum family coverage deductible plus the maximum catch-up contribution amount (for 2019, $6,900 plus $1,000 = $7,900). However, your bank is not required to distinguish between HSAs with individual versus family coverages — rather, your bank should apply the same total maximum to all HSAs.

For resources related to our guidance, please see:

IRS Form 5305-B, Health Savings Trust Account, Article I (Rev. December 2011) (“1. The trustee will accept additional cash contributions for the tax year made by the account owner or on behalf of the account owner (by an employer, family member, or any other person). No contributions will be accepted by the trustee for any account owner that exceeds the maximum amount for family coverage plus the catch-up contribution.”)
IRS Form 5305-B, Health Savings Trust Account, Article III (Rev. December 2011) (“It is the responsibility of the account owner to determine whether contributions to this HSA have exceeded the maximum annual contribution limit described in Article II. If contributions to this HSA exceed the maximum annual contribution limit, the account owner shall notify the trustee that there exist excess contributions to the HSA. It is the responsibility of the account owner to request the withdrawal of the excess contribution and any net income attributable to such excess contribution.”)
IRS Notice 2004-50, Health Savings Accounts (HSAs) (“Q-74. Is the HSA trustee or custodian responsible for determining whether contributions to an HSA exceed the maximum annual contribution for a particular account beneficiary? A-74. No. This is the responsibility of the account beneficiary, who is also responsible for notifying the trustee or custodian of any excess contribution and requesting a withdrawal of the excess contribution together with any net income attributable to the excess contribution. The HSA trustee or custodian is, however, responsible for accepting cash contributions within the limits in Q&A 73 and for filing required information returns with the IRS (Form 5498-SA and Form 1099-SA).”)
IRS Notice 2004-50, Health Savings Accounts (HSAs) (“Q-73. Is there a limit on the annual HSA contribution which the trustee or custodian may accept? A-73. Yes. Except in the case of rollover contributions described in section 223(f)(5) or trustee-to-trustee transfers, the trustee or custodian may not accept annual contributions to any HSA that exceed the sum of: (1) the dollar amount in effect under section 223(b)(2)(B)(ii) (i.e., the maximum family coverage deductible) plus (2) the dollar amount in effect under section 223(b)(3)(B) (i.e., the catch-up contribution amount). All contributions must be in cash, other than rollover contributions or trustee-to-trustee transfers. See section 223(d)(1)(A).”)
IRS Instructions for Form 8889 (2018) (“The maximum amount that can be contributed to your HSA depends on the type of HDHP coverage you have. If you have self-only coverage, your maximum contribution is $3,450. If you have family coverage, your maximum contribution is $6,900. Note. If you are age 55 or older at the end of your tax year, you can make an additional contribution of $1,000.”)