Facing a budget deficit of as much as $600 million for the next fiscal year, D.C. Mayor Vincent C. Gray has asked accounting giant Deloitte to analyze the District’s public schools budget in search of savings and new sources of money.

The city spends more than $1 billion a year on K-12 education — $750 million for 123 public schools and $400 million for 52 public charter schools — by far its biggest ticket item. Gray said in a brief interview that Deloitte, which will do the analysis on a pro bono basis, will look for “savings to be had and money to be found.”

Kaya Henderson, the interim public schools chancellor, has signaled that the city’s diminished financial condition will mean smaller school budgets and in some instances larger class sizes.

Officials were scheduled to inform individual schools of their 2012 budget allocations last month but have delayed the process to look for more money. In addition, Chief Financial Officer Natwar M. Gandhi’s office said last fall that the school system is projected to overspend its special education budget by more than $30 million in the current fiscal year. Henderson has disputed that analysis.

Linda Wharton Boyd, the mayor’s communications director, said details of Deloitte’s involvement are still being worked out. But the plan is for the firm to complete its study and have recommendations ready before Gray must submit his proposed budget for 2012 to the D.C. Council on April 1.

“We have to make some cuts and everybody has to share in the sacrifice here,” she said. “We need to be sure and we need to be accurate on what we can do to save costs.”

A Deloitte spokesman declined to comment. But one particular area Deloitte will examine, Wharton Boyd said, is the school system’s effectiveness in securing Medicaid reimbursements for services provided to students with disabilities. Although officials say the process has improved, poor tracking of cases and paperwork miscues have resulted in claims that the federal government has disallowed.

As D.C. Council chairman, Gray frequently expressed frustration about the opaque character of the school system’s finances, which are not routinely audited. Responsibility for budgeting is split between Gandhi’s office, which keeps the books, and the chancellor, who runs the public schools. The division, a legacy of the District’s Control Board era, has led to confusion and interagency finger-pointing.

Last year’s collective-bargaining agreement between the city and the Washington Teachers’ Union was nearly scuttled because Gandhi and former chancellor Michelle A. Rhee could not agree on how much money the city had to fund the contract. Several days after Rhee stunned the council by disclosing a $34 million budget surplus, Gandhi said the books actually showed a $30 million deficit.

Wharton Boyd said Gray wants to make sure that his first budget submission as mayor is completed without “smoke and mirrors.”

Deloitte would not be the first outside accountants to uncover nasty surprises. In 2007, new Mayor Adrian M. Fenty hired New York-based Alvarez & Marsal to scrub the school budget. The firm announced that the school system was on track to overspend its budget by $155 million.