Thirteen city charter schools are suing the state comptroller, Thomas DiNapoli, pushing back against what appears to be a campaign by Mr. DiNapoli against the city Education Department.

Mr. DiNapoli this week told the department he is launching an audit of its practice of awarding no-bid contracts, financial arrangements that are made outside of the normal competitive bidding process. The contracts have risen substantially in number since Mayor Bloomberg took control of the city schools in 2002.

The state comptroller’s office has also been ramping up its oversight of charter schools authorized by the Department of Education, seeking to audit not only their finances — as Mr. DiNapoli does for schools across the state — but also their academic performance.

Charter schools are public schools that operate outside most ordinary regulations.

The audits, initiated last summer, have been halted after a group of 13 of the schools filed a lawsuit against the comptroller, charging that Mr. DiNapoli’s inquiries were out of his legal bounds.

“He wanted to start going into all the schools and asking for non-financial information,” the policy director at the New York Charter Schools Association, Peter Murphy, said. “It’s just more regulatory creep that we believe is completely unwarranted.”

The association and a city center that assists and advocates for charter schools, the New York City Center for Charter School Excellence, are financing the schools’ legal push and are parties to the lawsuit.

Mr. DiNapoli’s office has defended its audits. In a letter to the charter school group last fall, a lawyer in the comptroller’s office, Albert Brooks, said auditors want to look at whether charter schools have met their self-designed targets for test performance, and to examine the schools’ processes for admitting students.

Charter schools admit students through random lotteries but are often criticized for “creaming” the best students from conventional public schools.

Mr. Brooks said the two areas “have clear fiscal implications for the public as well as the governmental entities that fund the charter schools.”

Mr. DiNapoli’s targeting of charter schools authorized by the Department of Education follows an audit by his office, released in September, of the department’s oversight of charter schools, which Mr. DiNapoli portrayed as lax.

City school officials said they had already corrected many of the noted flaws by the time his audit was published.

A spokesman for the education department, David Cantor, declined to comment on the lawsuit against Mr. DiNapoli. The department is not a party to the suit.

Mr. Cantor also had no comment on a second audit now being begun by Mr. DiNapoli’s office on the department’s no-bid contracts.

The city’s public advocate, Betsy Gotbaum, suggested the comptroller perform the audit, a spokesman for Mr. DiNapoli said.

Ms. Gotbaum has joined several elected officials in criticizing the contracts, which have awarded more than $270 million to outside consultants since 2002.

Mr. DiNapoli is a Democrat who was elevated to the statewide comptroller post by his colleagues in the state Assembly after the elected comptroller, Alan Hevesi, pleaded guilty to a felony of defrauding the government in connection with his use of a state driver to accompany his wife.