The service said in a statement that it treats domestic incidents seriously, but feels it's important "that the views of complainants are also taken into account when making decisions in such cases."
Bale, who denies the allegation, said through his spokeswoman, Jennifer Allen, that he was relieved the issue had been settled.
The actor "hopes to put the matter firmly behind him" and will be providing no further comment, Allen said in a statement released by Bale's lawyers.
His family had previously declined to comment, saying the issue was a personal matter.
British media had reported that Bale's mother and sister told police he assaulted them at his suite at the luxury Dorchester Hotel on July 20, a day before he attended the European premiere of his film "The Dark Knight." Bale has denied the accusation.
The Sun tabloid reported that police waited a day to arrest Bale so he could attend the film's premiere in London's Leicester Square. He was questioned for several hours at a police station before being released on bail.
The Wales-born actor first made a splash in 1987 as the child star of Steven Spielberg's "Empire of the Sun." He has played dark and sometimes sinister roles in such films as "American Psycho," "The Machinist" and "Batman Begins."
In "The Dark Knight," Bale reprises the role of wealthy playboy Bruce Wayne and his crime-fighting alter-ego Batman, a brooding vigilante superhero still scarred by the murder of his parents.
Bale, 34, lives in the Los Angeles area with his wife, Sibi Blazic, and their young daughter.
