The principal of a Queens middle school twisted teachers’ arms to vote for joining a pet program of Chancellor Carmen Fariña, and launched a revenge campaign after peeking at the secret ballot, a probe found.

Principal Zoi McGrath wanted JHS 67 in Little Neck to become a so-called PROSE school, in which administrators can bend city rules to adopt innovative practices. McGrath told teachers the school could get an extra $1.5 million, which was false.

The ballot was supposed to be secret, but McGrath and an ally, teacher Ruta Dave, knew how teachers voted and “pressured” those who voted no to change their votes, the city’s Special Commissioner of Investigation found.

McGrath, 69, even sent her daughter to a teacher’s home to drop off another ballot, says an SCI report.

While several teachers did reverse their no votes, it wasn’t enough. So the “vindictive” principal closed a staff parking lot, cut off access to a copy machine, and threatened to do more teacher “observations” — giving one who voted no a bad rating, faculty members told the SCI.

Of 60 staffers, 25 voted no and 35 voted yes, or 58 percent. To pass, 65 percent must approve.

But the whole vote was pointless because a DOE panel had already rejected the school’s plan “on its merits,” officials said. Under the plan, which sources say was poorly devised, all 7th- and 8th-graders would take advanced arts classes for high school credit.

The DOE called the alleged shenanigans “concerning behavior,” adding that McGrath and Dave, who denied wrongdoing, each received “a letter to the file.”

McGrath retired following the SCI probe, and took home $180,288 last year, records show. She declined to comment.

“The school’s application was denied on the merits of its proposed plan before any official vote was possible,” said DOE spokesman Michael Aciman.

“The PROSE program helps build stronger school communities, and we have a detailed process in place to ensure schools selected for the program have a track record of innovation and collaboration.”

The DOE has named 140 PROSE schools and plans to increase the number to 200 in several years. PROSE stands for “Progressive Redesign Opportunity Schools for Excellence.” Officials said selected schools get no extra cash.