The state Board of Library Commissioners last week weighed in on the debate over amendments to the state budget aimed at preventing four library closures in Boston.

In a memo to lawmakers, chairman George Comeau and the commissioners said they were "deeply concerned" with the amendments. The amendments, attached in both the House and Senate versions of the budget but being worked out in a conference committee, demand that the Boston Public Library system keep all branches open, or else money will be withheld.

Library trustees voted in April to close four branches, including one in Lower Mills. They cited the economy and a "vision" to modernize and strengthen the library system.

"This language, intended to preserve Boston branch libraries, will likely have unintended negative consequences for libraries and patrons statewide," the library commissioners wrote of the amendments.

Echoing a similar memo from BPL officials during the legislative debates over the budget, library commissioners argued that the amendments would limit access to the libraries.

If the BPL doesn't receive state aid, it would not be required to lend materials to other libraries or serve residents in other communities. The memo states that 34 percent of Boston library card holders live outside of Boston.

"The MBLC greatly appreciates the Legislators’ efforts to keep libraries funded and open so that our residents can access vital services, but the budget language referred to above could have a wider negative impact that would limit patron access across the state," they wrote.

Lawmakers say they have offered to plug the budget gap, but have not received solid assurances from library officials that the money would keep the libraries open.