During the radio interview, Ackerman said she was "pressured to hire" Michael Masch, the district's chief financial officer, and that she had asked him to step down to no avail.
"He was responsible for all of the district's operations. . . . It's curious that he would still be there," she said, alluding to the district's budget woes.
Ackerman also said that Mayor Nutter, who had described her as emotional, had made a "sexist comment."
"I'm not emotional. I'm clear of mind, clear of thought," she said. "I don't have to mince my words."
School district spokesman Fernando Gallard said yesterday that the district's attorneys are trying to determine if the remarks violate Ackerman's separation agreement.
She also spoke critically about district officials and Nutter in interviews with Fox 29 and Education Week.
Ackerman is owed her $905,000 settlement by Wednesday.
The potential stumbling block was first reported yesterday by the Inquirer.
"I think the SRC might request that their general counsel write to her lawyer and issue a warning," said former interim district CEO Phil Goldsmith.
"She could say that they're violating her First Amendment rights. But on the other hand, she voluntarily signed the agreement."
Other headaches could loom on the horizon for Ackerman involving her former communications staff.
City Councilman Bill Green said he wants state Auditor General Jack Wagner and City Controller Alan Butkovitz to investigate whether three members of Ackerman's staff had helped coordinate rallies in her favor and done other behind-the-scenes work while on the clock.
The allegations were reported on Tuesday by City Paper.
Butkovitz said last night that the controller's office isn't permitted to do performance and management audits of the district.