You may sue animal control but doing so can be very difficult and complicated.
This is because animal control services are provided by the government or through a contract with a humane society. As such, animal control may have sovereign immunity under state law, depending on the circumstances of the case.
That means that the question of suing animal control rests on whether sovereign immunity applies to your case.
In California, state laws offer sovereign immunity, which protects government entities and employees from personal liability.
An analogy may help to clarify this situation. If the police fail to arrest or detain a suspect, that does not automatically mean you can sue them. The same applies to animal services if they fail to capture a snake that bit you.
Still, there may be cases where the government waives sovereign immunity. In those instances, you can sue the relevant government agency. This includes cases where a government entity failed to protect its citizens due to a breach of duty.
One example is the 2011 case of Pierce County animal control in Washington. A pit bull attacked a local resident. Animal control was held liable because they had failed to declare the pit bull dangerous even after several visits to the victim’s home. This case has been appealed, but may be useful as precedent in similar situations.