At Tuesday night’s finance committee meeting, the Board of Aldermen’s budgeting process for the next fiscal year gained momentum.

Aldermen heard testimony from representatives of various city departments at the meeting regarding their 2012-’13 budgets and considered the best way to allocate New Haven’s budget in the wake of an economic recession. While most departments came before the committee with budgets similar to years past, those that proposed increases in funding faced increased scrutiny from aldermen.

The budget Mayor John DeStefano Jr. proposed last month — which spends $486.8 million, up 2.4 percent from last year’s total — served as a blueprint for the committee. DeStefano’s budget includes a $2.7 million increase in police department funding and a $1.2 million increase in education funding, which would be the first such increase in four years.

When he released his budget proposal, DeStefano said these increases are possible in large part because of a $7.5 million increase in property tax revenue.

With DeStefano’s budget as a starting point, the finance committee will continue to hear testimony from officials and city residents before drafting and voting on its own proposal. The full Board of Aldermen will likely vote on a final budget in May.

In the past, the board has been considered a rubber stamp for the mayor’s fiscal policies. But last fall, aldermanic candidates endorsed by Yale and city employee labor unions defeated many DeStefano-backed candidates to win a controlling majority on the board, which may allow them to set the tone of this year’s budget discussions.

The budget for the mayor’s office decreased $2,000 from previous years in DeStefano’s proposal, in part because of layoffs in the department over the course of the past decade, said Rebecca Bombero, DeStefano’s legislative director.

During her testimony, Sally Brown, a representative from the town clerk’s office, explained that the $1,000 increase in their budget — which has been denied for a few years — would go toward nonvital office supplies. Like the groups that preceded her, Brown sailed through the committee with few questions from aldermen.

But when acting city assessor Alexander Pullen asked the board for an increase from what DeStefano had allotted him, he faced resistance and increased questioning from the committee. Pullen said his department needed more money in order to cover costs for property revaluation as well as to print legally required documents his office had been unaware it needed to have in hard copy.

Yet DeStefano’s budget proposal denied him these increases, keeping the assessor’s funds near past years’ levels.

“[The cut] will impact us greatly because the assessor’s office requires a lot of technically skilled positions — in addition to having to generate revenue for the city we have to be in state compliance,” he said. “The more that we have to focus on state stuff, the less we can focus on generating revenue.”

After hearing from city attorney Victor Bolden and Michelle Duprey, director of the city’s Department of Disability Services, both of whom said their departments have faced drastic cuts in recent years — Duprey is the only employee in her department — acting comptroller Michael O’Neill testified for the city’s Department of Finance.

When he announced his budget, DeStefano emphasized that the largest increases in city expenditures came from growing pension and health care costs for city employees — both of which are handled by the Department of Finance. Despite O’Neill’s department only requesting an increase of only 1 percent in its budget, the finance committee spent nearly two hours questioning O’Neill about the cost-effectiveness of Department of Finance initiatives. Ward 10 Alderman Justin Elicker, Ward 9 Alderwoman Jessica Holmes, Ward 7 Alderman Doug Hausladen ’04, and Ward 5 Alderman and Board President Jorge Perez encouraged O’Neill to find additional savings for the city in health care and debt service costs.

The next meeting of the finance committee, where testimony from city departments will continue, will take place Thursday at City Hall.