All Massachusetts residents eligible for Chapter 62F refunds should receive paper checks in the mail or via direct deposit within the next two weeks.

The Baker administration is in the final stretch of distributing nearly $3 billion in excess revenues back to taxpayers through a 1980s tax cap law known as Chapter 62F.

About $2.5 billion had been returned to 2.9 million taxpayers as of late last week, a state official told MassLive Thursday.Read more: Mass. tax refund formula flawed, checks will be too high, new report claims

Roughly 1 million refunds totaling $600 million were issued via direct deposit, the official said. Another 1.9 million refunds totaling $1.9 billion were sent as checks in the mail, a distribution method the Baker administration has warned may result in some delays from the U.S. Postal Service.

Refunds will equate to about 14% of an individuals 2021 personal income tax liability, which critics say is a regressive formula that leads to the states highest earners receiving the largest returns. Low-income residents who do not pay income taxes, or whose income liability was reduced to $0 due to intercepts such as unpaid child support and other debts, will not receive a refund under Chapter 62F.Read more: Passage of millionaires tax has higher ed leaders seeking expanded access to state colleges and universities

No action was required to obtain the refunds, as long as taxpayers filed their returns by mid-October.

Bay Staters who believe they are eligible for the refunds should not worry if they have yet to receive theirs, a state official has told MassLive. But if its yet to arrive by Dec. 15 the final date the Baker administration has outlined for the distribution process people can contact the states 62F Refund Call Center at 877-677-9727. It is open on weekdays from 9 a.m. to 4 p.m.Read more: Healey touts Mass. climate resiliency push as she welcomes Royal Family

The call center cannot provide taxpayers with their individual refund amount, though a state webpage about Chapter 62F does offer a refund estimator tool.

The Department of Revenue does not initiate contact with taxpayers by email, text messages or social media channels to request personal or financial information, the webpage states in bold font. Note that there is no system through which you can check the status of your 62F refund.