Sutton Police has arrested a 33-year-old man after blood splatter and a discarded knife were found on Sutton Green.
Officers are investigating to see if any offences have been commited.
The force was called at 8:35am yesterday morning after a passerby made the discovery on a bench at the High Street park.
The area was cordoned off while police forensic experts investigated.
Police used a blood dog, which smells the blood that has been left and will hunt for more.
Officers contacted local hospitals to see if they had admitted anyone with a knife wound.
If you have information you can contact police on 101 or the charity Crimestoppers on 0800 555 111.