DETROIT — Detroit’s police chief stepped down Monday after a week of embarrassing revelations about a sexual relationship with a subordinate, forcing the city to search for a fifth leader in four years for a department dealing with one of the nation’s highest violent-crime rates.
Ralph Godbee was hired two years ago to replace a predecessor fired following an affair with a female officer who allegedly also had a relationship with Godbee. His departure extends the revolving door of leadership in a cash-strapped city.
Detroit’s next chief will be its 10th since 1991, and several of those were forced out amid allegations of wrongdoing.
‘‘Not having a stable head makes the rest of it unstable,’’ Isaiah McKinnon, a former Detroit police chief, said of the musical chairs in the city’s top cop’s office. ‘‘The officers are going to go out and try to do their jobs, but you need a stable head.’’
Godbee stepped down after married internal affairs officer Angelica Robinson said she and the married chief had a yearlong sexual relationship. It was the second alleged tryst with a subordinate to surface against Godbee since he became chief in 2010.
Robinson posted a photo on Twitter of her with a police gun in her mouth. Her lawyer, David Robinson, said the photo was posted after she learned Godbee was at a police conference a week ago in San Diego with another woman. He said Godbee had other officers locate Angelica Robinson and put her under surveillance.
There was no mention of the scandal in an eight-paragraph letter Godbee sent to Mayor Dave Bing announcing what was described as a retirement. Bing insisted he did not push the 25-year veteran to leave but called it the right decision.
‘‘He was very contrite, I think embarrassed,’’ Bing said at a news conference. ‘‘He felt he had let me down. He felt he had let the department down. He felt he had let the citizens of Detroit down. We’re not perfect individuals, and a lot of us make mistakes.”
As the city begins its search, police rank-and-file are becoming more vocal about a 10 percent pay cut and 12-hour work shifts enacted near the end of Godbee’s tenure. Bing’s office contends those cuts and others are necessary to help reduce a budget deficit of more than $200 million.
McKinnon, who led the Police Department for four years in the mid-1990s and resigned to teach at a university, said the city should also look outside the ranks for its new chief.
‘‘Detroit, traditionally, has been somewhat of an enclosed city,’’ McKinnon said. ‘‘For some reason, we are reluctant to bring outsiders in . . . particularly in law enforcement.’’
Godbee’s predecessor, Warren Evans, was dumped by Bing in 2010 for taking part in a promotional video for a cable police reality show. Bing later said he also fired Evans because the chief was romantically involved with a lieutenant. It later was learned that Godbee also had a relationship with that female officer when he held the rank of assistant chief.
A year earlier, Bing fired chief James Barren after less than a year on the job. Bing said Barren did not do anything wrong, but that he felt the department needed a leadership change.
Bing, who tapped 38-year police veteran Chester Logan to lead the department in the interim while a search is being conducted, said another change at the top should not reflect poorly on the department’s 2,600-plus officers.