A 26-year-old man was arrested after the incident in the Butter Market, North Street, Chichester, last Tuesday.
A 40-year-old man and his dog were both left with wounds after being bitten.
The owner of the bulldog, who is from Cheshire, was arrested on suspicion of failing to keep a dangerous dog under control.
He will return to answer his bail at Chichester police station today when he will be quizzed again by police.
The bulldog was seized by Chichester District Council dog wardens and was destroyed with the owner's agreement.
Insp Di Lewis, head of Sussex Police's dog unit, said: 'We work closely with councils across Sussex to take action against owners who do not keep their animals under control. All police dog handlers are trained to deal with dangerous dogs and work with dog wardens.'
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