Yes. You are responsible for keeping your dog under control at all times in public, and are liable for injuries which it causes to people or animals. You can also be fined for failing to have effective control - I understand up to $1,100 (or $11,000 if your dog has been declared a dangerous dog).
If your dog has a tendency to pursue and attack other animals, I suggest you get appropriate obedience lessons, ensure a proper control lead, have someone suitably in control walking them, and invest in a muzzle.