On weekday afternoons, city residents trickle into the basement of the New Haven Public Library, making their way down the stairs, past the circulation desk and the computer clusters until they greet a Yale student at a makeshift desk who asks them for photo identification and hands them a double-sided form, English on one side and Spanish on the other.

The form is the 2013 Volunteer Income Tax Assistance Client Form, and the student is a greeter for Yale VITA, a branch of the national Internal Revenue Service program that helps low- and moderate-income people complete their annual tax returns free of charge.

On Monday, after just 22 days open thus far this season, Yale’s branch of VITA helped its clients procure a total of over $515,000 in tax credits and refunds, already matching its half a million dollar record from tax season last year. The primary credit for VITA clients is the Earned Income Tax Credit, said Sam Hamer ’13, who founded the program at Yale in 2011 and continues to volunteer as a tax preparer.

The EITC is a tax refund available to working families earning less than $51,000 per year. According to a report of the New Life Corporation, a New Haven-based nonprofit consumer financial protection organization, $360,000 went unclaimed under the EITC in 2010 by eligible New Haven families. Each year, an average of 20 percent of credits are never received by eligible tax filers, according to IRS estimates.

The VITA program first took off in New Haven in 2001 at the behest of Mayor John DeStefano Jr., said Rick Kaiser, a board member of the New Haven Economic Security Coalition. The clinics aim to help residents take advantage of the full force of available tax credits. New Haven residents may currently benefit from both the federal EITC and the Connecticut EITC, which was first implemented in November 2011 and hailed by Gov. Dannel Malloy at the time as a means of putting an additional $108 million into the pockets of the state’s working families.

But as VITA programs gather momentum — saving New Haven clients a total of $6.4 million in refunds and credits in 2012, as estimated by the Connecticut Association for Human Services — those credits themselves are now under siege by state budget cuts. The governor’s current budget plan may slash the two-and-a-half-year-old state credit that complements the federal EITC.

Malloy has proposed lowering the amount of money the state pays back to families in the form of tax credits — from 30 percent to 25 percent of the federal EITC, or from $1,767 to $1,473 per household. The modification, which may only be for a two-year period, will depend on additional rounds of state budget negotiations.

Lucille Sclafani, VITA coordinator at CAHS, said the nonprofit organization is working to prevent those cuts.

“We understand that they’re going to do a little trimming, but we want to make sure that the state EITC doesn’t get chopped,” she said. “We don’t want them to see the credit as someplace where people can say, ‘Oh, we can cut even more spending here.’”

Sclafani said she will be working with lobbying groups to try to persuade the governor and the Legislature to preserve the state EITC as they hammer out a final budget deal.

Still, Yale VITA members say they have high hopes for their project. The program is staffed by 67 IRS-certified tax preparers, all of whom are Yale undergraduates except for three law students, said Ariella Kristal ’14, who coordinates the program along with Amalia Skilton ’13.

Ajanae Grant, a senior at Southern Connecticut State University, attended the clinic on Friday to inquire about receiving additional federal student aid credits.

“I’m not an expert on taxes,” she said as she waited in line. “And I don’t have the money to pay someone to do this for me.”

With increasing manpower, Kristal said the program is setting new goals. She said she hopes they will break a million dollars in refunds and credits by the end of the tax season on April 15.

Jan. 25 marked EITC Awareness Day, an event sponsored by the Connecticut Association for Human Services to raise awareness of the state and federal income tax refund.