The vote Tuesday was 6-3.
Crittendon has been criticized by legal experts, the judge and Detroit Mayor Dave Bing for going "rogue" for acting against the wishes of the mayor.
She had argued that the consent agreement is a violation of the city charter which prohibits Detroit from contracting with entities in debt to the city.
Bing had previously asked Crittendon to resign from her position, arguing she exceeded her authority when she penned the lawsuit aimed to derail the city's agreement with the state.
Under Detroit's City Charter, a two-thirds majority of City Council was needed to remove the Corporation Counsel, who is appointed by the Mayor.
During the presentation Bing said Crittendon was in the job when he became mayor.
He told City Council that he wanted the opportunity to appoint his own Corporation Counsel.
Detroit City Council mulls more cuts to save city's budget
The Detroit City Council is meeting to discuss further cuts that will save the city from financial disaster.
Bing addressed the council Tuesday asking for quick action on seven measures to balance the budget.
One includes suspending pension credits for employees for one year, more furloughs, layoffs and selling of assets.
Detroit faces a deficit of at least $200 million and has been struggling to maintain cash flow.
Council President Charles Pugh said he wants the council to go through the committee process, which means a vote that could be delayed until next week.
Meanwhile, a state-appointed review team is going over the city's books to determine if an emergency manager is needed.
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