DETROIT – Detroit Mayor Dave Bing was elected to replace a scandal-plagued predecessor after promising to clamp down on crime. But after allegations of a sex scandal involving another police chief, he’s having trouble stabilizing the department, let alone the streets.

Bing suspended Police Chief Ralph Godbee, 44, after a subordinate, a 37-year-old internal affairs officer, claimed the two had engaged in a sexual relationship for about a year.

The mayor hired Godbee two years ago after firing his predecessor, in part because of similar charges involving a subordinate. Bing knew at the time that Godbee previously had a romantic relationship with the same woman, a police lieutenant.

Should Bing’s investigation conclude that Godbee too must go, the city would be forced to seek its fifth police chief in four years. In Bing’s three-plus years in office, he already has fired two chiefs.

“He’s had more people resign, fired, quit than any other mayor that I know of,” Councilman Kwame Kenyatta said Wednesday. “It either says he chooses the wrong people or doesn’t know how to choose the right people.”

Like many police departments, Detroit’s force is under severe financial constraints. The city has about 2,700 officers, down from 4,000 a decade ago.

The department reports most violent crimes numbers are down this year, but the city also is on track to eclipse last year’s 344 murders. Robberies at gas stations and convenience stores, including the assault and carjacking of a prominent pastor, are becoming more violent and brazen.

“The officers are working 24/7 and aren’t being treated well,” said Oakland County Commissioner William Dwyer, a former Detroit police official. “They’ve taken dramatic cuts in salaries and benefits. They are in the most dangerous city right now in the U.S. If you expect them to perform, you ought to treat them like professionals and not second-class citizens.”

Even before the alleged scandal came to light, Bing and Godbee have been at odds with officers over a 10 percent pay cut, health care premiums and 12-hour work days.

This year, the chief reduced staffing inside police precincts to get more officers on the streets.

“The more immediate issue facing people in Detroit are the screaming headlines about the number of people shot or injured, and the fact that the number seems to be on the increase as opposed to the decrease,” said Sheila Cockrel, a political analyst and former councilwoman. “Detroiters are going to want a police chief focusing on those issues and not what’s happening in his personal life.”

Angelica Robinson, the internal affairs officer who says she had a relationship with Godbee, posted on Twitter a photo of herself with her service weapon in her mouth, her attorney said. She had learned Godbee was at a weekend police conference with another woman. Godbee had other officers locate her and surveil her, the attorney said. She has been reassigned from internal affairs and does not have her service weapon.