The 20-year-old defender was questioned by police after the alleged assault of a man, thought to be 18, in Hale, Greater Manchester, at around 12.30am on Christmas Eve.
Richards was arrested by appointment at a police station on Wednesday has been bailed until April.
He is the second Manchester City player to be arrested in recent days. Last week the Brazilian star Robinho was arrested over allegations an 18-year-old woman was raped in a nightclub in Leeds.
Yesterday Mark Hughes, the Manchester City manager, said the club would do everything to support Richards, and said he could be involved in Saturday's home game against Middlesbrough.
He said: "We are very supportive of Micah. He went to the police station in a pre-arranged appointment. It is an ongoing situation, we are aware of that and we are supportive of him."
Asked whether the defender was in the right frame of mind to be considered for selection this weekend, he replied: "Absolutely."
If you buy something from an SB Nation link, Vox Media may earn a commission. See our ethics statement.