The two teenage boys who were injured in the incident remain in a stable condition in hospital.
There are unconfirmed reports that this may have been a stabbing incident, but North Yorkshire Police are still describing it as an assault which left the boys "seriously injured."
Police are not looking for anyone else in connection with this incident.
Detective Chief Inspector Dave Ellis, of North Yorkshire Police, said yesterday: "I understand this incident may cause some concern in the local community. However, at this time we are not looking for anyone else in connection with this incident.
"Local officers will be in Harrogate today, as enquiries continue, and to provide reassurance to the public."
There was a heavy police and emergency services presence at the Valley Gardens on Saturday, including firearms officers as a precaution. Police were called to the gardens at 3.30pm.
Anyone who witnessed the assault, or has any information about it, is asked to contact North Yorkshire Police on 101, select option 2, and ask for Harrogate CID, quoting reference NYP-13042019-0299.