He said Godbee had other officers locate her and put her under surveillance. She has since been reassigned from internal affairs to other duties and does not have use of her service weapon, David Robinson said.
On Tuesday, Bing said in a statement that he suspended Godbee for 30 days from his $140,400-a-year post "pending a full and thorough investigation of this matter."
Assistant Chief Chester Logan has assumed Godbee's responsibilities during the suspension.
Godbee, returning to Detroit after attending a police conference out of state, told reporters Wednesday evening at Detroit Metropolitan Airport that he could not comment on Angelica Robinson's claims or his suspension.
Bing has spent much of his first term as mayor cleaning up the fiscal mess and $300 million budget deficit left by ex-mayor and convicted felon Kwame Kilpatrick. He's also changed the perception of a City Hall warped by public corruption.
However, his handling of the police department has been spotty, Kenyatta said, pointing to the firing of ex-chief Warren Evans that led to Godbee getting the job.
Bing appointed, Evans, a former Wayne County sheriff, as police chief in 2009 but fired him after he took 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 Lt. Monique Patterson.
Godbee also had a romantic relationship with Patterson before she began dating Evans and when she was Godbee's subordinate.
The relationship between Godbee and Patterson was made public after Godbee was named interim chief. Bing subsequently issued a statement insisting he wouldn't fire Godbee for having an affair with a subordinate.
At the time of his firing, Evans was spearheading an apparently successful police blitz on crime hot spots across the city.
Godbee joined the department in 1987 and rose to assistant chief in 2007. He later retired only to be reappointed assistant chief in July 2009 when Evans was hired.