City and state principals have joined teachers in challenging the state Education Department’s authority to dictate how educators are evaluated, The Post has learned.

Their unions argue that state law requires that most details of new teacher evaluations be negotiated between unions and local school districts rather than set by the department — something an Albany judge agreed with this summer.

But while the ruling applied only to teachers, state officials — who appealed it — have agreed that final court decisions would cover principals as well.