On March 10, the New York Education Department announced the release of the third version of Proposed Regulations (full text) to assure substantially equivalent instruction for non-public school students. According to Hamodia:
These regulations, like the those previously proposed, require periodic reviews of every nonpublic school by their LSA (local school district or authority).
Where they differ is that they offer a few paths for a nonpublic school to avoid those reviews, at least initially. One such path is “registration” — which is the technical term for a high school that administers the Regents examinations. Another is “accreditation” by an agency that is approved by the State Education Department....
Our analysis is that all of the non-Jewish private schools will be exempt from LSA reviews while a majority of yeshivos will not be exempt. As a result, these regulations governing the substantial equivalency reviews by LSAs will be applied exclusively at yeshivos.