MAYOR MARTY WALSH quickly sought to stabilize the Boston Public Schools in late June by tapping local education nonprofit leader Laura Perille as interim school superintendent to replace Tommy Chang, who exited abruptly with two years left on his contract in the face of mayoral displeasure with his tenure. But that move is now running into some serious shoals of its own.

The Globe reports that nearly a dozen educator, parent, and civil rights groups are calling on Walsh and the city’s School Committee to declare that Perille will not be a candidate in the search for a permanent superintendent for the district. Rev. Willie Bodrick II, a leader of one of the groups, told the Herald that the groups fear good outside candidates will be reluctant to apply for the post without clear assurance that Perille won’t be in the pool.

Asked about the request following last night’s School Committee meeting, Perille declined to say whether she plans to seek the permanent position. A spokeswoman for Walsh said the mayor would review the letter from the groups but said he will “defer any comments” on the search process to the School Committee.

Michael Loconto, the committee chairman, told the Globe last night that he hadn’t yet a chance to read the letter. But Hardin Coleman, the School Committee vice chairman, told the Herald it would be unfair to bar anyone from applying for the job, a move that he said would be “autocratic.”

Though the School Committee is formally in charge of the search and ultimate hiring of a superintendent, the reality is that how this is all handled will be the mayor’s call. He appoints School Committee members under the city’s mayorally-controlled school system.

Perille, who ran the nonprofit EdVestors, has been a well-respected figure in local education circles. She does not, however, have direct experience as a classroom teacher, school principal, or school district administrator. Several large urban districts have looked outside traditional circles for superintendents in recent years, tapping everyone from former business executives to ex-military leaders to bring fresh perspective to the challenge of improving big school districts. Perille would also bring one thing Chang and other superintendents hired through big national searches lacked — a detailed understanding of the complexities and politics of the Boston school system.

Boston has had experience in recent years with interim superintendents tasked with steering the district for periods of time. But both of those who’ve served recently in that role — John McDonough and Michael Contompasis — were nearing the end of their careers and made it clear they were not interested in the permanent job. (Contompasis can’t quite seem to fully retire, however, as he was recently tapped by the state to serve as receiver of a chronically struggling Boston elementary school.)

In Perille’s case, the fact that there has been no similar declaration certainly seems to suggest that she could become a candidate for the job. Globe columnist Joan Vennochi went much further than that, writing in early July at the time of Perille’s appointment as interim superintendent, that she is Walsh’s favored choice and “the permanent job is hers to lose.”

How this will play out is anyone’s guess. What’s certain is that Walsh — who is also fending off criticism over late and missed school bus trips — is learning that with the power of mayoral control of the schools also comes all the problems and tough decisions.