Sgt. turned Detective Harvey Bullock and Detective McGonigle were pains in the backsides of the Batmen. And yet, these obese officers had the best of intentions.
Bullock was on the trail of Earth-One's Batman, who's vigilante methods were against Harv' own personal credo. Restrained by Police Commissioner Gordon, Bullock begrudgingly worked alongside Batman on a few cases.
McGonigle had a different take on Earth-Two's Batman, approving of and even admiring the dark knight's detective work. Seeking to emulate it brought him into conflict with the Catwoman on her first case, and other team ups with the Dynamic Duo of Gotham. Eventually, he left for Empire City and assisted (both in an out of his superhero costume) police officer Dan Richards aka the original Manhunter, wherein he gained a bit more clout.