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Students from Celia Cruz Bronx High School of Music, where Principal William Rodriguez faces discipline after an investigation, performed Friday at Grand Central Terminal.

A Bronx principal is facing discipline after investigators substantiated allegations that he played fast and loose with school funds.

The Special Commissioner of Investigation looked into allegations, first filed in 2011, that William Rodriguez, the founding principal of Celia Cruz Bronx High School of Music, billed the city for time he did not work. Investigators substantiated at least some of the allegations and delivered a report to Chancellor Dennis Walcott last month.

Asked about the report on Friday at Grand Central Terminal, where Celia Cruz students were performing to celebrate the station’s centennial, Rodriguez said he had not been found guilty of any wrongdoing. “Nothing has been substantiated,” he said.

But Department of Education officials were already deciding how to act on SCI’s findings.

“We are in the process of determining discipline,” Connie Pankratz, a department spokeswoman, said on Friday. A spokeswoman for the Council of School Supervisors and Administrators confirmed that Rodriguez met with the union’s grievance department on Monday, a standard step whenever a school employee is facing sanctions, which could range from a fine to termination.

Teachers, staff, and students at the school say that whatever misconduct investigators found would be merely a symptom of deeper leadership problems. They say Rodriguez, an accomplished musician himself, poured school resources into Celia Cruz’s award-winning music program while leaving students without adequate preparation for college.

“Please don’t let the many accolades our students receive in music fool you,” one person at the school wrote in 2011 to State Comptroller Thomas DiNapoli, who monitors the state’s finances and investigates fraud. “The principal is out of touch with the needs of the students and staff. I’m begging you to please look into this matter.”

Among the allegations that investigators looked into was that Rodriguez forged time sheets to be paid for portions of the school day when he was not working and for work he did not actually do outside of school hours.

Copies of Rodriguez’s overtime timesheets from the 2010-2011 school year, which GothamSchools obtained, show that at a time when schools across the city were slashing their budgets, Rodriguez filed for overtime pay for attending student performances, high school fairs, and after-school music classes — expenditures that multiple other principals told GothamSchools are usually the first to be cut.

At a rate of roughly $44 per hour, Rodriguez took home more than $5,000 for the time, on top of his $150,000 annual salary.

The timesheets also show that Rodriguez did not punch in and out using a time clock on regular school days or have handwritten records approved by his supervisor, an option allowed when work is done off-site. Instead, he handwrote his timesheets and had the school’s business manager sign off on them. In their complaints to the city and state, staff members said they thought Rodriguez did not actually work most of the hours.

They also said Rodriguez asked a school employee to help out with his personal business during school hours. And they said Rodriguez’s side gigs, a weekly piano performance at Willie’s Steakhouse and a teaching gig at nearby Lehman College that a city spokeswoman said had been approved by the department’s ethics officer, sometimes distracted him from Celia Cruz.

On the evening of March 17, 2011, for example, Celia Cruz held parent-teacher conferences while Rodriguez was scheduled to teach a music history class at Lehman. “I brought a parent and another teacher to his office, and it was locked and it was dark,” one staff member said. “And that parent was angry.”

All of the teachers and staff members interviewed requested to remain anonymous out of fear of retaliation. But they said that while they were concerned about the possibility that Rodriguez was appropriating some of the school’s funding, they were more worried about other issues at the school that are not grounds for a city investigation.

Teachers, staff, and students said Rodriguez favors the school’s arts programs, which by all accounts are outstanding, but gives short shrift to academics, particularly math and science.

Students who enroll find a robust arts program with more than a dozen different ensembles, including an award-winning choir and a Latin music band that performed last year before Mayor Bloomberg’s State of the City address. More than 70 percent of the students who entered in 2008 graduated last year with a special arts designation on their diplomas, according to Department of Education data.

But just 18.9 percent of the students were college-ready, compared to 30 percent citywide. At the Brooklyn High School of the Arts, which also has an arts focus and enrolls very similar students, the college-readiness rate was 25.6 percent. Celia Cruz’s data took the biggest hit in math, where students’ average Regents exam score in Geometry and Algebra II was well below the 65 required for graduation.

On last year’s department survey, 73 percent of Celia Cruz teachers said they disagreed or strongly disagreed with the statement, “The principal places the learning needs of children above other interests.” Ninety percent said they disagreed with the statement, “The principal at my school participates in instructional planning with teachers.”

Sources at Celia Cruz said an external grant is the only way the school can pay for Regents exam and SAT preparation classes and after-school tutoring. At the same time, the school budget funds a summer music camp, which enrolls middle school students in hopes that they’ll apply to Celia Cruz.

The summer program is open to “anyone and everyone” and is funded through overtime payments and grants, according to Assistant Principal Jerrod Mabry. “We find the money to make it happen because it’s so important for our outreach,” he said in 2011.

And while school funds support students’ travel to state music competitions, academic teachers rarely get help paying for field trips, teachers and staff members said. A history class’s planned trip to Washington, D.C., was canceled in 2011 because Rodriguez was unable to provide bus fare after students raised funds for their hotel rooms and activities, they said.

Two years ago, when she found that the school was cutting its part-time college advisor, whom staff members said worked for free in the application-heavy month of December, Janel Strachan, a 2012 graduate, said she grew so concerned about the school’s direction that she sent an impassioned plea for help to Schools Chancellor Dennis Walcott.

“Not many of us would like to continue music after high school, and [we] are very concerned with our academics,” she wrote in the 2011 letter.

Until this year, the 438-student school had five music teachers and just three math teachers, where schools of this size have four math teachers. Strachan said her junior-year trigonometry class contained students who had passed the previous math course and also students who had not. The teacher essentially taught two classes at once, but all students got the same credits, she said.

“The admissions offices at the colleges I apply to are going to expect me to know trigonometry,” she said at the time. “But when I take the placement exam, I will fail.”

Now a first-year student at the University at Albany, Strachan said her fears have come to pass. In her first semester, she earned A’s in her music classes but D’s and C’s in science classes. She squeaked by in a basic statistics class by taking it pass/fail.

“New information was introduced to me and a lot of other people knew it already,” she said. “It made me feel pretty bad.”

This year, the school increased the number of math teachers to four and decreased the number of music teachers, also to four. But the most challenging math class at the school remains Algebra II/Trigonometry, according to department officials.

Teachers and staff members say students could be doing better if Rodriguez adjusted his priorities, or if a new principal brought a more even-handed approach to the school.

“We have an amazing music team — they’re so talented,” a staff member said. “Even if he cut a position or some resources, we’re still going to get a fine music program.”

Additional reporting contributed by Sarah Darville and Emma Sokoloff-Rubin