Sec. 7.5-203. Civil Litigation.
The Corporation Counsel shall defend all actions or proceedings against the City. The Corporation Counsel shall prosecute all actions or proceedings to which the City is a party or in which the City has a legal interest, when directed to do so by the Mayor.

Sec. 7.5-204. Penal Matters.
The Corporation Counsel is the city prosecutor and shall:
1. Institute and conduct, on behalf of the people, all cases arising from the provisions of this Charter or city ordinances and, when authorized to do so by law, cases arising under state law.

Sec. 7.5-209. Enforcement of Charter.
The Corporation Counsel shall be responsible for enforcing compliance with the Charter. Corporation Counsel shall document in writing any violation of the Charter by the executive or legislative branches, Office of City Clerk, elected official or other persons subject to compliance with the Charter. This written notice shall contain the nature of the violation, including the Charter section(s) violated, direct the necessary action to be taken to remedy the violation, and date by which the remedial action must be taken. The time for taking the required remedial action shall not exceed fourteen (14) calendar days. The notice of Charter violation shall be presented to the offending body or individual, with a copy provided to the Mayor, City Council and City Clerk. In the event the offending body or individual fails to remedy the Charter violation within the time frame and manner required in the written notice, Corporation Counsel shall take all reasonable actions to secure compliance, including, but not limited to, judicial action.

Crittendon cannot rely on section 203, since she is barred from "prosecut[ing] all actions or proceedings to which the City is a party or in which the City has a legal interest," unless she is "directed to do so by the Mayor."  The mayor has publicly stated his disapproval of the lawsuit, so I think it is safe to say he did not direct Crittendon to file it.

Section 204 appears to provide independent authorization for Crittendon to act on her own and to command her to act -- "The Corporation Counsel . . . shall institute and conduct. . ."  But section 204 expressly relates to "Penal Matters," meaning criminal violations of city ordinances or charter provisions.  Black's Law Dictionary defines "penal" as "punishable; inflicting a punishment; containing a penalty, or relating to a penalty."  An action seeking a judgment declaring whether a contract is enforceable is not "penal" and, therefore, not a proper subject for unilateral action by the city's counsel.

Section 209 comes the closest to justifying Crittendon's position, but it falls short because it is obviously written to permit the city's counsel to enforce charter compliance internally, within the city government.  It could be argued that, since the city council approved the consent agreement, allegedly in violation of the charter, Crittendon is doing nothing more than securing the council's compliance.  The case, however, is City of Detroit vs. Michigan Treasury Department.  If the case was really all about forcing council to comply, it would be captioned Corporation Counsel vs. City Council, or something similar.  Section 209 does not apply to external entities.

Even if an arguable case can be made for Crittendon's actions, how can she square her lawsuit with section 210:

Sec. 7.5-210. Claim Reduction.
Corporation Counsel shall advise City departments, agencies and entities on risk reduction strategies that are necessary to limit or eliminate the City's exposure to liability.

By filing this lawsuit, not only has Crittendon not acted to "limit or eliminate the City's exposure to liability," she has increased exponentially the possibility of an even greater financial crisis than currently exists.