Investigators who look into the city’s schools received more allegations and opened more cases than ever last year. But they found wrongdoing less often than at any time in the last decade.

And once again, only a tiny fraction of the investigations were made public.

The Office of the Special Commissioner of Investigation received 4,173 complaints in 2012, 20 percent more than in the previous year, according to the annual report it released today. The complaints prompted 795 investigations.

SCI looks into alleged violations of law and department regulations, from accusations of sexual misconduct to concerns about fraud and embezzlement, to allegations of cheating on tests. (The Department of Education also has an internal investigative unit, the Office of Special Investigations.)

In 2012, SCI also closed 752 cases, many opened in previous years because SCI investigations frequently move slowly. Of them, investigators found wrongdoing in 247 cases for a substantiation rate of 32.8 percent, the lowest in a decade. Condon recommended that 83 education department employees be fired as a result — 20 percent fewer than in 2011.

Condon’s office released just 16 investigation reports, meaning that 94 percent of times when investigators found wrongdoing, their findings stayed under wraps.

The release rate was in line with past years, when SCI has published reports about substantiated allegations between 5 and 10 percent of the time.

Last year’s SCI releases included reports about nepotism, corruption, and sex abuse. It did not include any reports about cheating or academic improprieties.

In a year with a spate of high-profile sexual abuse allegations in schools, the unit received 679 allegations of sexual misconduct, or 16 percent of the total number of allegations. That proportion was in line with recent years.

SCI reports that are not published are sent to Schools Chancellor Dennis Walcott, who has the power to act on Condon’s recommendations or take other steps to address wrongdoing. At that point, the only way for a report to become publicly available is via a Freedom of Information Law request. That means that an enterprising reporter, advocate, or elected official would have to know first that an investigation happened, and then would have to file a legal request for permission to look at the report on it.