Three struggling Long Island schools were among 73 statewide named Monday as eligible for state funds that would help them operate as community hubs dispensing medical, nutritional and legal aid as well as educational services.

Some local education officials, however, voiced reservations about the state’s “community schools” plan, saying that strings Albany attached to the money could prove an impediment.

Schools on the Island identified as eligible to share in the initial $75 million in grants include Hempstead High School and Alverta B. Gray Schultz Middle School, both in the Hempstead district, and Milton L. Olive Middle School in Wyandanch. All schools named would have to apply for the money.

The announcement followed a unanimous vote Monday by the state Board of Regents, establishing rules for eligibility.

Mary Jones, superintendent of Wyandanch schools, said in a phone interview she would welcome a chance to apply for grant money.

But Jones objected to a state requirement that an administrator be assigned in each community school to coordinate the various services offered, suggesting the rule was overly bureaucratic.

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“From the little I know about it so far, it’s an extremely difficult proposal,” she said. “It takes so much to operate a community school.”

In Hempstead, the new school board president, Maribel Touré, said she had not been briefed on details of the grants, but found the general approach appealing. Touré added that she would check with the district’s new interim superintendent, Fadhilika Atiba-Weza, to see if a grant application would be feasible.

The concept of community schools has been floated in New York State for more than 20 years and already has had some success in New York City and in other states, such as California and Texas.

The idea behind the approach is that students in schools with high rates of academic failure often suffer from poor health and nutrition or other problems, and that those issues must be addressed if they are to have any chance of improving their schoolwork.

Gov. Andrew M. Cuomo and state lawmakers approved the extra $75 million in school funding in April. That followed action taken a year earlier, setting up a new system of identifying schools that were struggling academically and setting penalties for those that did not improve within a year or two.

In addition to the administrative requirement, districts wishing to operate community schools must meet with parents, teachers and others at least four times during each school year to solicit suggestions on planning and running such programs. Districts also must offer early childhood education programs and provide space within schools for health examinations and other services.

Regents Chancellor Betty Rosa of the Bronx, who once served as principal of a community school, called the approach a “lifeline for families.”

Another board member, Roger Tilles of Great Neck, who represents Long Island, also voted for the eligibility rules but said he thought the role of the school site coordinators should be better defined.

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“I’m just a little apprehensive about what this person’s role would be,” Tilles said.