ALBANY — A bill that would allow all of New York’s school boards to mandate that students attend kindergarten at age 5 has passed the Senate and Assembly.

It is not yet headed to Gov. Andrew M. Cuomo’s desk for consideration.

Cohoes and Watervliet, have imposed such a requirement under existing state law, but the proposed measure would extend that power across the state.

Districts that impose the mandate would be able to call county social service workers who could ultimately charge parents with educational neglect if their kids aren’t in school.

“It gives us leverage,” Watervliet Superintendent Lori Caplan said of the requirement. Watervliet offers early and universal pre-K for 3- and 4-year-olds.

But by the time kids turn 5, some may not show up for kindergarten. The fear is the students would lose momentum after two years of pre-K on reading lessons and more. While it’s a local decision, kids in most school districts are supposed to be in kindergarten if their fifth birthday arrives by Dec. 1.

Calling county social services or child protective services would be a last resort, Caplan said, after school officials first reach out to a family with phone calls and visits to see why their child hasn’t started school.

The other communities that currently require kindergarten attendance are New York City, Syracuse, Rochester, Utica, Buffalo and Yonkers.

The new legislation provides a mechanism for keeping students home for a year if their parents want it. And families would still be able to send their children to private or parochial schools, or home-school them.

There have been debates over the best age to start kindergarten. Parents and teachers in Guilderland have discussed letting 4-year-olds start. State law currently requires compulsory schooling from ages 6 to 16; all districts in New York that offer elementary school also offer kindergarten.

“Studies show that students who attend kindergarten are better prepared for school,” according to a memo of support from the state School Boards Association. ” … Kindergarten should be treated as what it is, a critical part of the K-12 continuum. This change in policy would reinforce the importance of kindergarten, where important skills are taught.”

The legislation was sponsored by state Sen. James Skoufis of Woodbury and Assemblyman Michael Benedetto of the Bronx, both Democrats. Benedetto chairs the Assembly’s education committee.