Officers were called to Canbury Gardens to reports the birds had been targeted in the water, leaving one dead and one injured.
The injured swan was found washed up, exhausted, missing one eye and an X-Ray at the vets found a pellet lodged its skull.
On Monday 15th January, it was reported that another swan had been shot in Canbury Gardens.
Witnesses or anyone with information on these incidents are urged to call police on 101 or contact crime stoppers to remain anonymous.
