The woman reported that one of the two dogs bit her repeatedly in the face, hand and ankle, Misquez said.
Less than 10 minutes later, officers responded to a report of a second attack involving the same dogs about a block away in the 3000 block of Hudson Drive, according to Misquez.
The sergeant said a 46-year-old man walking his two small dogs reported that the pit bull and Labrador attacked his animals and when he tried to protect them, the pit bull bit him in the calf.
Both victims were taken to hospitals to be treated for minor to moderate injuries.
Misquez said officers were able to catch the Labrador retriever but struggled to catch the pit bull, which ran through the neighborhood, prompting police to advise a nearby preschool to shelter in place.
Police and Contra Costa Animal Services officers were able to contain the pit bull in a backyard, where it charged at them, the sergeant said.
Officers then had to use a Taser to subdue the dog, he said.
Animal Services officers took custody of both of the dogs and are investigating the attacks.
The dogs' owners were not at home at the time and the animals appear to have escaped an enclosed backyard, Misquez said.