Sir Richard Leese was arrested on Monday on suspicion of common assault.
The teenager was reported to be the Labour councillor's 16-year-old stepdaughter.
Police said the injuries to the girl were "very minor".
Nottinghamshire: Animal welfare groups criticised a plan to ban dogs from 72 park areas.
Newark and Sherwood District Council has put dog control orders in place in the areas in a bid to make sure people look after their pets.