At 8:16pm on Tuesday police received a number of calls of males seen with machetes in the park and reports of males being injured.
Firearms officers were deployed to the park and searched the area, with support from a National Police Air Service helicopter, but no injured parties were found and no suspects identified.
Around 200 people who had gathered in the park were dispersed by local officers who remained in the area.
Two males, both aged 17, subsequently attended at hospital with serious injuries that appeared consistent with having been assaulted with weapons.
Both have been arrested on suspicion of affray and are continuing to receive treatment in hospital for injuries that are not considered life threatening.
Detectives from Leeds District CID are continuing to carry out enquiries into the incident.