In both cases, county leaders say they were prompted by the death of Jacob Bisbee, who was killed by three of his his step-grandfather pit bulls in July.
It was not until 2005 that the state allowed local governments to take up the issue of breed specific ordinances.
"We're not hearing of Chihuahuas killing babies in our communities and in our cities and unfortunately this breed is very difficult in those circumstances," Supervisor Mary Piepho said.
Both boards of supervisors Tuesday voted to refer the idea to the proper committee or next step which will involve public input before any proposed ordinance is drafted.
There was some early public input Tuesday morning in Santa Clara County where many people do not like the idea of a mandatory ordinance aimed at one dog type.
"I've said for years if we are to have anything mandatory, it should be mandatory dog training lessons," Karen Johnson, chair for the Animal Advisory Committee, said.
Many dog lovers say as tragic as the mauling death of Bisbee was, the blame is on the dog guardians and not the dogs themselves.
"All small children under the age of six should never be left alone with any breed of dog, period," Patricia Watson of the Northern California Terrier Association said. Watson was left with scars from a dog attack at age six from a small breed.
While the Human Society Silicon Valley supports the spaying and neutering of all animals regardless of breed, they do not support an ordinance aimed at any one breed. For one thing, they say such a county ordinance would be hard to enforce.
"I think it would be tremendously difficult to enforce in terms of what is an American Pit Bull Terrier or pit bull-type dog," Ali Talle, director of Behavior Programs at the Humane Society Silicon Valley, said.
In Santa Clara County, the supervisor who proposed looking into the matter points to San Francisco's mandatory spay and neuter ordinance for pit bull type dogs.
Supervisor Ken Yeager sees the idea as a proactive approach to protecting public safety. Still he is willing to accept that a lot of research must be done and public input will guide what any proposed ordinance eventually looks like.
"I'll start off thinking mandatory, but after hearing from pit bull owners and others we might change our mind, but that's what we are going to explore for the next several months," Yeager said.