The State Education Department, after seeing a copy of “independent study” guidelines in use at Wadleigh and a number of other schools, said it was examining whether the practice met its standards. State law requires students to earn credits by completing set hours of “seat time”  essentially, showing up for class  and demonstrating subject mastery. To graduate, they must also pass Regents exams.

“We are looking into this situation very carefully,” said Johanna Duncan-Poitier, the senior deputy state education commissioner. “We want to make sure that the student is getting what they deserve.”

Critics say the practice is poised to become more prevalent as principals enjoy greater freedom from supervision at the same time as they are held more accountable for student performance, two hallmarks of Mayor Michael R. Bloomberg’s plan to overhaul city schools. Last fall, schools received letter grades based on student performance, with principals at D or F schools in danger of losing their jobs.

Diane Ravitch, a historian of the city’s public schools who has been a frequent critic of the mayor’s efforts, says the practice of credit recovery could raise questions about the validity of gains in the city’s graduation rate. According to the state, the city had a 50 percent four-year graduation rate in 2006, the most recent year for which data was available, up from 44 percent in 2004.

“I think when it’s used correctly, it might be a good thing,” Ms. Ravitch said of credit recovery, “but when used incorrectly it’s a way of gaming the system.”

But Mr. Klein said there was “no basis to suggest that improper credit recovery has affected graduation rates.” Saying that 39,000 students received Regents or local diplomas last year, 8,000 more than in 2002, when the mayor took control of the schools, he added, “A few anecdotes don’t materially affect this rise.”

Randi Weingarten, president of the United Federation of Teachers, said that the union had received “enough complaints about it that we are really concerned,” but that without hard numbers on the prevalence of credit recovery, she could not say whether the graduation rate was suspect.