It comes after reports that two 16-year-old males were shooting at birds in the park over the weekend.
Cleveland Police have now confirmed that they received a report of a person “believed to be shooting at geese” just before 9am on Saturday, November 20.
Hartlepool Borough Council have said that actions such as are “incredibly disappointing” and have asked people to respect and “enjoy safely” the town’s park spaces.
A council spokesperson added in a statement: “Unfortunately, we have removed three further Canada geese from Rossmere Park that appear to have been harmed.
“It is too early at this stage to say exactly how they have been targeted, but we do believe they have died from their injuries.
“Police have been informed and we would encourage anyone with information to contact the non-emergency number on 101.
“It’s incredibly disappointing that a small minority of people choose to behave in this way.
"Our parks are there for everyone to enjoy. By all means visit these local beauty spots, but please respect them and enjoy them safely.”
A spokesperson for Cleveland Police said: “Police received a report on Saturday 20th November, at around 8.45am of a person believed to be shooting at geese.
"We are working in partnership with Hartlepool Community Safety Team and inquiries are ongoing.”