A powerful aide to Mayor Michael R. Bloomberg resigned from City Hall because he was arrested in Washington, D.C., for his role in a heated altercation with his wife, according to a person familiar with the account. Stephen Goldsmith, who oversaw the city’s most visible agencies as Mr. Bloomberg’s deputy mayor for operations, was arrested in his town house on July 30 and spent two days in a Washington jail — a series of events that Mr. Goldsmith reported to City Hall almost immediately. Mr. Goldsmith’s 14-month tenure at City Hall was troubled from the start. He clashed with his fellow commissioners, upset municipal unions, and oversaw the city’s widely criticized response to a blizzard last December. Mr. Goldsmith, 64, who split his time between New York and Washington over the last year, had previously served as a two-term mayor of Indianapolis in the 1990s. There, he gained a reputation as a wonkish reformer who emphasized outsourcing traditional public functions to private industry. He has written several books on government innovation, tracts that helped land him a academic post at Harvard University, where he worked until Mr. Bloomberg recruited him to work at City Hall. Goldsmith received his bachelor’s degree from Wabash College and his law degree from the University of Michigan.