Residents are rallying in support of their branch libraries as city officials consider consolidations and the closing of an expected $3.6 million budget gap in the fiscal 2011 budget.

In Lower Mills, the head of the local merchants’ association is organizing a letter-writing campaign in a bid to save the local branch. Tony Paciulli, the president and CEO of Meetinghouse Bank, said it is the “most vulnerable one” out of the 26 neighborhood libraries.

The Lower Mills branch is one of seven located in the Dorchester and Mattapan area, the others being on Adams St., in Codman Square, Fields Corner, Grove Hall, Uphams Corner, and the recently-dedicated new branch on Blue Hill Ave. in Mattapan.

“The community is definitely behind this,” Paciulli said of his efforts. “Most of the merchants have posted petitions [in their stores].” Paciulli noted that two schools – the Elizabeth Seton Academy and one of the campuses of Pope John Paul II Academy – “rely heavily” on the library and use its computers.

At a Tuesday meeting of the library’s board of trustees that was heavily attended by residents from across the city, officials outlined the criteria for a potential branch closing. They include how many books and audio/visual materials are borrowed; how many people pass through the doors; how many computer sessions and public wireless sessions take place within the library; accessibility; electrical capacity and the amount it has for added technology; meeting room and parking lot availability; and how many other libraries are within three square miles of it.

The last criterion led one supporter of the Egleston Square library in Roxbury who was at the meeting to observe that some Dorchester libraries are in likely peril. Officials have stressed that no final decisions have been made on closings. “Every branch has a story,” said Boston Public Library President Amy Ryan. “We will review the story behind the numbers.”

The $16.7 million Mattapan branch, which opened last year, appears to be safe with Ryan calling it an “example of a 21st-century library.” Jeffrey Rudman, chairman of the trustees, added: “If we had our way, every branch would look like Mattapan…But that’s not the world we inherited.”

Rudman noted the decrease in state funding for local libraries, and urged supporters to lobby State House lawmakers, who are preparing their version of the fiscal 2011 budget. But Rudman added that even if the budget issues did not exist, he would still support branch closures. “The country’s broke. The commonwealth’s broke,” he said. “We’re stuck. We’re going to have to make hard choices.”

Many audience members at the meeting, which was held at the main branch at Copley Square, called for all branches to remain open, saying the fight over which branches to close will pit neighborhood against neighborhood. If you decide to close certain branches and leave others open, “it will be a mess in this city,” said Sarah Ann Shaw, a supporter of the Dudley branch.

Library officials say that while they’re faced with cuts, they see opportunities, including the chance to revamp an aging system and align it with its more technologically-adept Mattapan branch. Ryan said the system’s website is so frequently visited it could be called a sixth largest branch. “We can’t take a car designed in the 1970s onto today’s information superhighway,” she said of the system.

Rudman also ruled out mandatory charges for the use of the library. The façade of the main branch in Copley Square includes the words “Free to all,” he noted. But he also said the library has “to do better at fundraising.” He seemed skeptical when an audience member suggested selling some of the library’s lesser-used properties as a way to raise funds for the system. “Would you like us to hawk the Gutenberg Bible in New York?” he asked.