Cops shot dead a pit bull in a Staten Island park yesterday after a dog fight got out of hand, police said.

The chaotic scene erupted when a woman walked her unleashed dog at Schmul Park in Travis at around 1 p.m., cops said.

Her dog ran off to brawl with two other pit bulls — and the woman was bitten as she tried to break up the fight, said police.

A cop called to the scene shot and killed a dog who lunged at him, said police.

The injured dog owner was treated for hand lacerations at Richmond University Medical Center, officials said.