Devon and Cornwall Police is now hunting for the dog's owner.
"I was terrified for my life as well," campaign leader Karen Hawthornwaite says.
Armed police were sent to the scene in Sunningdale Court in the Southgate area of Crawley.
Police probe numerous dog attack reports, but no arrests have been made and a dog has not been seized.
Postal worker Katy Davies suffered tendon damage and puncture wounds after she was bitten by a dog.
The family pet was said to be sleeping under a car on a street when the dogs "brutally" attacked her.
A man has been arrested on suspicion of having a dog dangerously out of control, police say.
Police say the attack by two cane corso dogs "left people injured and understandably shaken".
Marie Hay, whose daughter and dog were attacked, wants stricter laws brought in for pet owners.
