Officers were called to Market Square in the city centre, shortly after 5pm on Tuesday, June 21 following reports of a disturbance.
A 19-year-old man sustained minor injures during the incident.
A 17-year-old boy was arrested on suspicion of assault, possession of a knife and a public order offence.
He was later released on bail.
A 16-year-old boy was also arrested on suspicion of assault.
He was later charged with criminal damage and assaulting and emergency worker in relation to a later incident in custody.
He has been released on bail to appear at Nottingham Magistrates' Court on July 6.
Inspector Andy Wilson, of Nottinghamshire Police, said: “Investigations into this incident are ongoing and we are keen to speak to any witnesses who have not yet come forward.”
Anyone with additional information should call 101, quoting incident 614 of 21 June 2022, or Crimestoppers anonymously on 0800 555111.