With cuts to his office looming after the demise of Cook County’s controversial soda tax, Assessor Joseph Berrios testified Friday about his efforts to shed positions in an office that is already down more than 30 percent.

The budget pressure comes as the office was sharply criticized following a Chicago Tribune investigation earlier this year that found widespread inequities in residential property tax assessments.

Potential budget cuts to the office raise additional questions about Berrios’ ability to produce fair and accurate assessments for the 1.8 million parcels that comprise the county’s property tax base.

Among other things, the Tribune investigation found that the assessor’s office overvalued low-priced homes while undervaluing high-priced ones. Known as regressivity, those errors caused homeowners in poor, mostly minority areas of the county to pay more than their fair share.

The investigation prompted legislation, an investigation by the county’s independent inspector general, and County Board President Toni Preckwinkle to commission a study of residential assessments.

That study, by the Civic Consulting Alliance, a nonprofit that provides pro bono services from private experts to government, also came up during the meeting. Cook County Clerk David Orr, who is not seeking re-election after seven terms, said earlier this week that Berrios was stonewalling the study.

He said Berrios had canceled two meetings that had been scheduled to get the study started, which prompted Commissioner Richard Boykin to question Berrios about it during Friday’s hearing.

“People are concerned and think the system is unfair,” Boykin said. “I just want to make sure we are being fair to every taxpayer across the county because minorities and poor people feel they are paying too much.”

Berrios denied that he’s delaying researchers conducting the study, saying he had even provided office space for the researchers.

Orr blasted Berrios during a press conference Thursday, where he endorsed the assessor’s Democratic Party primary challenger, Fritz Kaegi, an asset manager. Orr said that there was a “need to clean up” the assessor’s office. Berrios’ campaign has not responded to Orr’s endorsement of Kraegi.

At the county hearing, Berrios said he had found more than $2 million in savings by eliminating vacant jobs from the books, getting him close to the 10 percent in cuts county commissioners are seeking. Yet Cook County Budget Director Tanya Anthony said $1.7 million was already figured into the budget and, as a result, doesn’t count toward the 10 percent goal.

That means Berrios may need to find more positions to cut, a prospect he said could affect the ability of his office to get tax assessments done on time and handle appeals. Berrios said he was the first assessor to get the work finished on time in 34 years, saving municipalities, school districts and other taxing bodies across the county $5 million to $6 million a month.

“Can I live with this? Not really,” said Berrios, who is also chairman of the Cook County Democratic Party. “I cannot sit here and guarantee we can get the job done on time.”