A Department of Education official broke ethics rules when he told the principals he worked with that he planned to join a different organization that also supports city schools, according to a ruling out today from the city’s Conflicts of Interests Board.

The ruling highlights a fundamental tension in the Department of Education’s controversial “network” structure for providing support to schools.

Under the five-year-old structure, dozens of networks compete against each other for schools to hire them to provide instructional and operational support. Nonprofit groups outside of the Department of Education are allowed to compete, in an arrangement that is meant to keep networks mean and lean — and also lays a minefield of potential ethical violations.

Robert Cohen was leading a department-run network, Children First Network 104, last year when he got a job offer from CEI-PEA, a nonprofit group that works with dozens of schools through five networks of its own, according to the report. After he told the principals he supervised about the offer, they all applied to switch from the department-run network to CEI-PEA’s. That meant they would give their schools’ network fees to CEI-PEA, instead of keeping the funding within the department.

After the department granted permission to just 13 of the 31 schools that applied to switch, Cohen lobbied for them to be allowed to come back to their original network, and ultimately, he stayed at the department, too. But Cohen still ran afoul of city ethics rules just by implying that the schools might consider taking their business outside of the department in order to continue getting help from him, the conflicts board determined.

“While I was unaware of this at the time, I now acknowledge that my presentation to the principals … in my capacity as a future CEI-PEA employee constituted an appearance in violation of [the city rule that] states: No public servant shall, for compensation, represent private interests before any city agency or appear directly or indirectly on behalf of private interests in matters involving the city,” Cohen said in today’s ruling. He agreed to pay a $7,500 fine for the violation.

The ruling was one of two that the Conflicts of Interest Board released today about Department of Education-related matters. In the other ruling, a secretary at Brooklyn’s School for Democracy and Leadership agreed to pay a $6,500 fine for making about $35,000 in purchases from a school supplies company that her husband operates.